Where to go in London - without Kids?

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Dsis and I are going for a long weekend in London in June to celebrate her 40th birthday. We've prvisionally booked at the travelinn behind the London Eye, but would love some good tips on where to go etc from those of you 'in the know'. We definately want to do the art galleries, shopping and covent garden for a potter round, but am really looking for some good suggestions for nice (but not overly formal IYSWIM) places to eat etc. Sis has been v ill recently, so must be easily accessible by tube (not changing 5 times) or readily supplied with taxis. It's been years since I managed to get to London without kids, so have forgotten anywhere I used to know (& they've probably all closed down anyway!)
Thanks in Advance

Take a look at Borough Market (Fridays and Saturdays, less crowded on Friday afternoons) for delicious foodie treats and a lovely atmosphere. There is a Fish restaurant in the market but you can buy the most delicious "fast food" from some of the vendors and picnic in the gardens of Southwark Cathedral. The market is near the river and the Riverside Walk is traffic-free and very level. It might be a bit far for your sis though...
Since your day Marylebone High Street also has lots of fab little shops and nice places to eat.
Kew is looking sensational at this time of year and a river trip from Westminster Pier might be a nice idea...
I rarely get to eat out at posh places any more but there is a very nice Ozer (Turkish) on Langham Place near the BBC and Oxford Circus, and Moro and Villandry are also on my wish-list.
Hope you have a great time and she has a wonderful birthday.

Thanks Marina, Borough Market sounds great, also like the idea of a river trip.. Will have to get my little 'Visitors Guide to london' book out & check out where everything is (no sense of direction I'm afraid)
Keep 'em coming girls.