Here are some ideas
Pitcher & Piano is a good laid back wine bar with lots of seating, food etc where you could easily bag a table, or
Smollenskys on the Strand could also be really good as you can get a table & eat as well. It's a bar & grill & does cocktails. As I recall also reasonably priced and v close to the theatre.
or Gordon's Wine Bar is right by the Embankment Tube Station. I love it but it's very cramped and only sells wine, or Champagne Charlies wine bar, which is underneath Charing Cross station and very close.
Another idea, but a bit further is
Brown's in Covent Garden
or if you REALLY want to be poncey - the barat No. 1 Aldwych. But it's probably shockingly expensive! As would be the American Bar at the Savoy!
So....that's what I've come up with very quickly. There's also the Coal Hole on the Strand which is a massive pub, so we might struggle to find each other.