Macbeth will be on at Regent's Park until mid-Aug and Othello at the Globe (which was fab, but make sure you're on the rate seating above the crowds - climbing those extra stairs is worth it even if you are pregnant - I was 30 weeks when I went, and they are not that steep).
Am also looking forward to Gaslight at the Old Vic, as am a Patrick Hamilton fan, which is running from June to mid-Aug. There's a production of Saint Joan at the National, but I don't know what they are planning to do with it - still it is rare to see any Shaw, so it may be worth it. For comedy, do go and see The 39 Steps - it is a really good production and very silly, but there ain't much comedy out there, apart from the Shakespeare summer standards at the Globe and National.
Fidelio is on at the ROH throughout June, which promises to be good.
Know nothing about ballet except that the Swan Lake that is on at the ROH next week has been given mixed reviews.
Not much of a musicals' fan, myself, but the Boyfriend, also at Regent's Park should be good as it is an old standard.
But it does look like this summer will be a bit thin for good theatre itself - for example, the programme at the National is not that inspiring - but all the musicals are on for the tourists as ever over the summer, so if you like them, then you'll be spoilt for choice. Around The World in 80 Days is a Cole Porter musical that is on this summer at Sadlers Wells, but you wonder why it is so rarely performed, even if written by the master. But everyone I know has raved about Avenue Q, but I haven't seen it myself.
Hope that helps.