In reply to RubyB:
+1 to the "come to the UK for trad climbing, not for sport climbing" sentiment. I can honestly say that I've never yet climbed a bolted route in the UK and thought "wow, this route would really hold it's own against a classic in Siurana, Kalymnos or San Vito Lo Capo". The trad climbing on the other hand could go toe to toe with anywhere else in the world in terms of quality, quantity and concentration of routes, the only lacking factor is extreme length for those crave 1000m+ long routes.
I'd say the best two general areas (huge variety and spectacularly beautiful) to climb in the UK are North Wales (geographically speaking, an approximately 50km-each-side square at the north-west tip of Wales) and North West Scotland (geographically speaking, the isles of Skye and Lewis/Harris and everything within a few km of the coast on the W side of Scotland from around Torridon to the NW tip). There are many other areas with amazing climbing, including Cornwall, Pembroke, Cairngorms and Lake District, what you think is the "best" area is a lot down to personal preference.
I strongly suggest organising a partner before you arrive. Unlike Ceuse, Siruana or Sicilly, in the UK you cannot generally just pick up a partner at the crag/parking area and finding partners at shortish notice online can be frustrating.
I don't know what your transport arrangements are going to be like but I would say that being able to move around is important when you want to get as much climbing done as possible. The maritime weather of the UK (particularly the West coast where all the best climbing is) is quite wet and forecast reliability is often only good for the next day, beyond that it is more an educated guess than a prediction. Often you can get excellent sunny, dry climbing by moving a relatively short distance, common examples include: In North Wales, a short drive takes you from the rainy Llanberis pass to sunny Gogarth sea cliffs and in NW Scotland, a varying length of drive takes you from any area of rain to Reiff where the sun always shines, in defiance of any kind of weather science.
At the time you are here, you probably will not have too much truck with midges (they are generally bad July to Sept but will be out in more moderate numbers from May to Nov) but it is worth bearing in mind that cloudy, still weather that would otherwise be perfect for climbing can be turned into a living hell by an insect about the size of a pin head. A moderate intensity attack can be ameliorated somewhat by repellent but if they are really bad, relocating to a sea cliff or higher crag (1000m altitude is best) is mandated.
Overall you chose an excellent time to come. In Scotland in particular, the weather in May, while a little cooler, is generally much better than in the high summer months of July/Aug (and the midges are not such a problem).
Post edited at 18:22