I used to live in Pimlico. There are a lot of chains and cafes in the area, but one of my absolute favourite restaurants is just down Wilton Rd and around the corner from Victoria:
http://www.grumblesrestaurant.co.uk/ They usually have a vegetarian starter/entree, but it's definitely British menu with a sort of modern twist to it. Always awesome.
There's a tapas place over on Lupus street. I've not been but it seems pretty popular. It's a bit of a slog from Victoria though.
If you want Indian, Paradise on Denbeigh [about three shopfronts past the junction of Wilton and Warwich] is very good. Their butter chicken is incredible. We've eaten there a lot, and we've never been disappointed. I don't hesitate to recommend this place for a picky eater.
http://maps.google.co.uk/maps/place?oe=utf-8&rls=org.mozilla:en-GB:official&client=firefox-a&um=1&ie=UTF-8&q=paradise+indian&fb=1&gl=uk&hq=paradise+indian&hnear=0x4876046848c95cb7:0xa0eae30461e40b0,Lambeth&cid=2130195918526760258
There is a Cypriot/kebab place around the corner from the junction of Wilton rd and Warwick way which is fairly good. It's not our favourite kebab place, but it's up there. It's on Warwick Way, right turn if you're coming from Victoria Station. It's on the first block, maybe 6 businesses down. [Edit: I almost forgot, this place has the most beautiful men working there (usually). If that's something you'd like as a part of the dining experience, then totally go for it. ]
Seafresh on Wilton is okay for a sit down fish and chips place. It's a step above your average chippy. Their fish is usually very good, but their chips can be hit or miss.
There's a Brazillian place (sorry, can't remember the name) across from the Sainsbury's on Wilton Rd. Fairly decent. There's also a Turkish place where we've not eaten, right around Sainsbury's. You can rent hookahs there though. There's also Pimlico Fresh, which is good, but may not be open. It's sort of a posh cafe. There's also a (British) Tex-Mex place which can be good, but can also fall short.
If I could pick only one place to take someone from out of town in Pimlico, I'd definitely recommend Grumbles. Call to make sure they aren't fully booked though.