|IMO the best low teen climbing in CA (if not the US) is the alpine stuff in the Sierra, though May is early to be trying to get up there. Even if the roads are open, you should expect to have to deal with snow & ice on the approaches and descents, and possibly on the routes themselves (on ledges etc.). Don't underestimate ice in particular - a small patch can really ruin your day...
That said, so far this year has been a bust in terms of snowfall, so if the dry trend continues the rest of the wet season, the Sierra high country may start opening earlier than it usually does. For reference, here's a list of historical hwy 120 opening times: https://www.nps.gov/yose/planyourvisit/seasonal.htm (hwy 120 is labeled "Tioga" here, after the pass it crosses). Note that the last couple of years have tended to have heavier precipitation later in the water year (i.e. from late February into May), and this has a direct, negative impact on how quickly CalTrans can get the trans-Sierra highways (120 in particular) open.
A better bet would be to head to the East Side of the Sierra, perhaps via Lover's Leap / Lake Tahoe, as others have suggested - Echo Summit on hwy 50 is a lot lower than 120, and is kept open year-round. There is endless amounts of incredible, long moderate climbing over there, at a variety of latitudes and elevations (so you can pick your ideal temperature and/or avoid snow), and May can still be comfortable in the Owen's River Gorge too, if you decide you want to clip bolts for a day or two. Bishop is an ideal basecamp for an East Side trip - you're within striking distance of all of the best that the East Side has to offer.