I've climbed Gerber-Sink end of March before in good conditions. I've also bailed off of a few things in there during that same time window. (End of March is my spring break, work in education.)
I think the most important thing is to be flexible, as mentioned. You can get out in pretty marginal weather if avy hazard is low and you are prepared. Some other spots that should be on your list to check depending on budget/travel time available... Rogers Pass, Canadian Rockies, Glacier NP, Bitteroots, South-central Idaho Ranges, Tetons, Rocky Mtn NP, Oregon Cascades, Elkhorns, Sierra, Wasatch, Great Basin NP.
I've had great luck in the Canadian Rockies that time of year. Ice is fat and sticky, huge variety of routes, alpine is just coming into condition depending on the year, cheap hostels and lots of partners to be had if you're solo or your buddy needs an extra rest day. One year I climbed 4 days of ice including routes up to 1,000 ft of climbing, then did an 800 ft limestone sport climb on a south aspect, then did a solo ski tour to scope an alpine face which wasn't in, so went mixed cragging the last day... pretty fun. Also, very different from the Cascades in-terms of rock, avy/snow, types of routes. A great contrast to what we get here.