It's generally so warm at the moment that little bits of rain forecasted don't matter as much. Stuff at Cheddar like Pride Evans Cliff and The Wave could be fine. Anything at Avon is worth a look anyway, as you can usually just sit out showers in the car, pick a route that stays dry, or one that will flash dry. If Upper Wall is to cold, there's a lot more sport now, e.g. in the New Quarry. Leigh Woods Quarry 3 sport will probably be OK but it's a bigger walk. There are shelters to sit out rain. Quarry 2's overhanging wall (Evil Edna etc. ) might be a good shout but I've not been. Q5 would ordinarily be fine but it's banned until 30th June as the Main Wall Peregrines have moved there. Also the ticks are probably out in Leigh Woods by now until October ish.
Little Grey Wall at Frome Valley was dry a few weeks ago and does stay dry in showers. Much of Large Grey Wall was still drying but Hubble and a few others are probably OK. Bourton Combe is probably fine.
The bottom of Wintour's leap (North Wall and GO wall) can be surprisingly sheltered too. Shornecliffe can stay dry in light showers this time of year, as can Owl Rock at Goblin Combe, and I suspect Wyndcliffe itself for more full on trad.