If you're into science & thinking of visiting the civilised part of London Greenwich, the Old Royal Observatory (& planetarium) are well worth a visit. The Cutty Sark would be brilliant for a 5 & 7yo - there's a stamp trail for children on the way round, they can try out various spaces onboard, and the collection of figureheads tends to fascinate. The Maritime Museum is good too (& has a fun children's gallery).
As PPs have mentioned, you can walk under the Thames at Greenwich; there's a Thames Clipper stop there (am pretty sure the tourist boats run down there too, but clippers are faster & cheaper); & you can pick up the DLR either side of the foot tunnels - if you sit at the front you can pretend to drive...
The park at Greenwich is beautiful - visiting the deer in the flower garden is one of my Brownies' favourite things when we're there. Even taking into account the fact there's a very nice playground... it is, of course, a huge park, so you need to be prepared for that!
Greenwich has lots of restaurants plus heaps of food stalls on the market at the weekend so there's plenty of choice of food available.
Oh & while talking about this corner of London, the Museum of London Docklands is great - less sciencey, but well worth visiting (& also has a brilliant children's gallery). It's on the way up towards Canary Wharf (think the DLR is South Quay).
Honestly, the tube with children the age of yours isn't awful - you're not trying (I'm assuming you'd have provided this kind of information...) to manage a pushchair & you have a hand available for each (you can walk sort of folded together). I don't know all the routes I take my Brownies on & we're from one of the tubeless bits of Inner London so they're not used to getting about by tube & we can't hang on to all of them. Being ready to move to the side while you check which exit you need from a platform & remembering to keep left in passageways & stand right on escalators is the key. There are lots of staff at stations who'll happily help you figure out your journey (though things are pretty clearly signed, I think). The TFL website's journey planner provides really detailed plans for you too - you can set it to just plan bus journeys if you really don't want to do the tube though.