Peckham is quite rough if you are a tourist and has no tube. checkout the travellodge website they are cheap and its best not to cut corners when you have a young one. or try etap or formula one.
the docklands are a good place to stay that is close to the city look at all the hotels near the DLR.
you wont need a carseat everything is easy to gte to via public transport. tubes and tube travellers do not like strollers you wont get any sympathey. you need to be able to collapse it fully and carry it most times. Sometimes your journey will be easier by bus or DLR.
get the weekly travel card its cehaper than everything else.
stone henge is far and easier by car but it would be expensive unless national express can take you its the coach service. its is difficult to get to and covered in wire to protect it. you cant near enough to touch it.
skip stone henge and go to York it is on a direct train route you can walk from the train station and its so full of history..If york is too far then try cambridge thtas great too
london things to do
Hyde park speakers corner sunday only - people stand on soap boxes and say alsorts its fun.
South bank
Shakesperes globe theatre
regent street and oxford street for shopping.
Richmond (zone 4) its very pretty and old england go and sit out by the thames and watch people in their boats.
london eye its really cool
covent garden see the street artists and they have markets on the weekend with handmade unique things.
Camden lock - markets and general hangout place of everyone cool. Great on a weekend - take cash!
oh little tip china town is good but only eat in the ones with lots of chinese people in them they are the only good ones.
haagen das cafe in leicester square is very good too and packed!
walk from Covent garden via leicester square to piccadilly its not far and easier than tube.
go to the 'tkts' booth in leicester square for 1/2 price tickets, the others are not as good. See who is on at the theatre!
eat at wagamammas its a really fun experience and celebs go there too!
Check out all the places I mentioned on websites before you go for opening times etc
have lots of fun its the greatest city in the world