Most streets are quite walkable, and you can see many places that are closeby just by walking! :) There are mostly metro, train, tram, bus, ferry etc. access everywhere. My suggestion is starting at eminonu, and taking the T1 tram to sultanahmet
See stations here
You can start at sultanahmet square. From here, sultanahmet mosque, Basilica Cistern, Topkapı palace and Hagia Sophia are all at a walking distance. For other such places, such as Grand Bazaar, Istanbul University etc. you can take the T1 tram and easily get there in a few minutes (or walk if you want to!)
I'd also suggest taking walks in Taksim (Europe side) and Kadikoy (Asia side). Kadikoy is less frequently traveled by tourists, but it's a great urban environment and there's much to see there, even when walking randomly. You can reach kadikoy by taking the ferry on eminonu.
I'd also suggest getting an Istanbul Kart (Istanbul Card), which is an all-round public transportation boarding pass. If you plan on using public transportation, it'll be very useful.
You can get one at major transit stops such as the airport, Sultanahmet, or Eminönü. To buy an Istanbul Kart, you need to pay a non-refundable 10 TL fee (for the actual card and the service), and of course an amount of your choice to load onto the card. 5 pass, 10 pass,etc. cards are also sold, but getting a card will be cheaper.
If you want a walk by the sea or nature, see here
Alternatively, there are many tourist groups on the sultanahmet walking route I mentioned. You can search for walking tour guides in that area before traveling.