Brooklyn to Cowan - Hawkesbury River station is close

This site is exactly what you’re looking for: https://www.sydneyhikingtrips.com/

If you have a little more time, the RNP from Bundeena. Via a train to Cronulla and ferry to Bundeena. The commute would be about 2.5 hours round trip. Leaving not a huge amount of time for your hike.

It's likely just outside your 4 hour limit, but there are some walks into the lower Blue Mountains national park from Glenbrook station.

Modern bushwalking in NSW started during the Great Depression in the 1930s, when walking was the only past time anyone could afford, and very few people had access to cars. So lots of historical tracks start from stations and places like Katoomba, Glenbrook, Wondabyne, and Otford.

And in fact the cutoff time for one of the original ultra trail running courses (the "Three Peaks") was to start from Katoomba station arriving on the Friday night "Fish" commuter train, and finish in time to catch the last Sunday night train back to Central in time for work on Monday!

Train to Engadine or Heathcote, Hike to Karloo pools.

4 hour on public transport or 4 hours including the walk itself?

This is a decent list to start with: https://weareexplorers.co/walks-near-sydney-train/

There are plenty of station to station walks in Kuringgai along the Great North Walk, otherwise there's Waterfall to Heathcote in RNP. If you are into trail running then 4 hours is possible total return, but if you want to walk then there's always Maroubra headlands.

Spit Bridge to Manly walk - bit of uphill then downhill.

Bus put to The Spit to start, then get a cheep harbour cruise home on the ferry.

All within 4 hours is a bit spicy. Honestly you're going to need to budget some more time. I love living in the inner west but the disadvantage is you're not as close to nature as you would be living in Engadine!

There are a few walks in the National Park easily accessible by train - the Karloo Pools walk is excellent with a good incline, it starts right from Heathcote station. Easily one of my favourites in the RNP.

Up north the Berowra Valley and Mt Kurin-gai-Chase national parks have good walks which are accessible from Mt Kurin-gai station. If you're feeling adventurous, packing a tent and hiking to the Crosslands campsite is a great way to spend the weekend. The campsite has toilets and fresh water and it's not a massive walk (though you can make it longer if you need).

Finally the Maroubra to Malabr costal walk is nice - that's once you could feasibly do in 4 hours or so, but it doesn't leave much time for fish&chips!

Something closer would be the Two Valley Trail in Woli Creek. That's 13km in total but pretty flat mostly. Great for trail runs though!

There are no walks that have all three traits of: commute, hike and return within 4 hours of the inner west; coastal; and incline.

I used to live in Ashfield/Summer Hill area and my recommendations are, however:

Spit to Manly (commute is train and bus to the Spit then ferry and train from Manly). Walking time is about 10km/3 hours and it's both coastal with inclines to the cliffs. The commute is probably an hour each way though.

Two Valley Trail from Bexley to Campsie via Wolli Creek. You can do part of this walk within 4 hours and it's 'coastal' as in 'by the river' but very flat.

Circular Quay to Watsons Bay (part thereof) might give you a walk that's within 4 hours including commute, while being satisfactorily coastal and inclined. It's not very inclined but I'm not sure what your criteria is (e.g. do you have a number in mind for elevation gained?).

There are a few decent walks in Lane Cove National Park that are pretty up and down. North Ryde and Macquarie Park metro stations are both nearby but I don't know how far the tracks are from the stations

Karloo pools/ Uloola falls and surrounds has lots of great walks that are all accessible via Heathcote train station. For a longer walk there's the Olympic pool which is this gorgeous big natural rock pool, which is great for a swim.

The Cape Banks from La Perouse walking track is accessible by bus, it’s a solid 8km round trip with a little elevation and very beautiful

There's a walk that starts directly behind heathcote station into the national park. Takes you to karloo pools and further to a waterfall I can't remember the name of. Plenty of up and down so a good workout. Haven't done it in a while but was great when I did.

https://share.google/egrxqzsk0MYUvNZvB

Hope that link works for you

Bays, points and reserves of the lower north shore. No major climbs but it's up and down all the way as you follow the foreshore as closely as possible. If it was a cycle race, it would be one for the puncheurs.

A few interesting sites like the Coal Loader, Kirribilli & Admiralty Houses, and Sub Base Platypus along the way.

Yacht clubs and cafes en route if you fancy refreshments.

Ferry to Cremorne Point Wharf then walk to Greenwich Wharf. Around 15km. You can stop for a swim at Greenwich baths at the end, which has decent change rooms and hot showers. Or, if you start at the other end, finish with a swim at MacCallum Pool at Cremorne Point, which is quaint but without facilities.

There's a nice one that starts at Stanwell Park station. You get a good leg workout on this.

https://www.nsw.gov.au/visiting-and-exploring-nsw/locations-and-attractions/wodi-wodi-walking-track

https://discoverhornsby.com/walking/blue-gum-walk/

Blue gum walk you can access from hornsby station

Berowra to Cowan along the Great North Walk track, specifically from the end of Turner Road. About 1.5-2hrs walking.

150m down into the valley and the same going back up. Up the hill to Cowan is a killer but absolutely fantastic for training, I know someone who does it weekly.

Buses in Berowra toward the start are every 30min and mostly line up with arriving trains. However trains from Cowan are hourly outside of peak, and make sure you are there a few minutes before the train leaves in case the crossing gates are down (a good motivator to keep pace :) ) but otherwise there is a nice cafe with food nearby if you do miss it.

If you ever want to extend it to a whole day, start at the Crowley Road trail at the roundabout ~500m from the station. The trail on from the car ferry at Berowra even has ladders!

Lane cove river/great north walk, pick a route between any two stations on t1/t9/metro. North Ryde to thornleigh is one of the longer ones. Alternatively Epping to Macquarie uni, cherrybrook to Hornsby 

We live in the inner west and did the Kamay Botany National Park coastal hike, only took us 30-40 mins to drive there from Marrickville.

Beautiful hike along the cliff edge and ended with a swim on an empty beach near Boat Harbor Beach

You can drop into the Lane Cove Nat Park from many stations along the north shore line, then walk out at a different station.

Cowan to Jerusalem Bay is a nice and low ish intensity and it’s beautiful only takes 40 mins one way - take swimmers

blue mountains is your best bet for actual incline. train to katoomba from central, giant stairway will absolutely cook your legs. or wentworth falls if you want something slightly less brutal

spit to manly is alright but pretty flat

Do the (Eastern Suburbs) coastal walk but start in Malabar.

The coastal walks are all fantastic. Pick a Beach and walk to Another Beach. North or South, doesn't matter, they are all awesome. Plus you can throw in a ferry ride.

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Girawheen park and the flying fox reserve are right off Bardwell park station or you can go from Turella to Bardwell. On days after storms there are small water falls.

take the ferry to taronga zoo. go on the short trail to Bradley's head then down to the beach

Darling mills

Wolli Creek bushland is a good quickie, train to Tempe

Sydney is pretty flat, finding walks with more climbing than the coastal trails isn't easy unless you hit the blue mountains. Maybe hit Waterfall and walk loops from there?

I presume you've done the cooks river as a walk? If you're willing to detour by road or bus a bit there's a walking track from Bexley North to Wolli Creek that drops out out near the fruit bat colony and it's an easy walk over the hill to Steel Park in Marrickville.

Likewise Paramatta River - you can train to Westmead and walk back to at least Leichhardt, or Circular Quay if you're keen.

There's also a walk along Georges River from Panania Station, walk west to the river then south/west along it until you get bored.

I mostly walk semi-randomly between parks and bush joining up smaller walks, so the short chunks like Bexley-Wolli don't bother me. There's an awful lot of half hour strolls that you can join up that way.