And the answer is this: May and June around here are really late winter in the mountains. In all likelihood, you're going to be camping on snow. Indeed, many trails may not be open, particularly if the general trend of a wet, cold winter holds up. And even into early June the chance of a snowstorm below the 5,000-foot level is surprisingly high.
For those reasons, I'm inclined to suggest either a four-season tent or a "convertible" tent that can be adapted as conditions dictate (that time of the year, it's quite possible to see highs in the 80s, snow, or a mix of both on the same trip). In the latter category, the Sierra Designs Omega ($290; www.sierradesigns.com) has a ripstop panel in the ceiling that can be zipped out if conditions warm up during the trip, to reveal ventilating mesh, or zipped out and left in the car. The same holds for the door. Either way, you have more control over ventilation within the tent than in a typical "three-season" tent, with their ample swaths of mesh. You can even leave some pole sections behind when it's calm.
Marmot calls their convertible tents "three-season extended" tents, and offers the Swallow 2P ($359; www.marmot.com). Same deal as the Omegathe ripstop panels can be left in place when it's cold and blowy, or unzipped in milder weather. Meanwhile, it has the same square footage as the Omega and is a little heavier (about seven pounds versus about six-and-a-half). But the Swallow does promise a bigger vestibule and a slightly more rugged tent on balance.
In a straight four-season tent, REI's Mountain 2 tent ($249; www.rei.com) is a winner: think good price, excellent features (including light aluminum poles and an efficient door-in-front design), and all-weather protection. Eureka!'s two-person Alpenlite XT ($200; www.eurekatent.com) is an often-overlooked bargain in a classic all-season tent. Here you get a rugged A-frame design and spacious vestibule, if slightly claustrophobic interior for long stays. And, if you plan to do a lot of these kind of trips, take a look at the Hilleberg Jannu ($595; www.hilleberg.com), which is a very light tent (just over five pounds) that you can take on an expedition or a summer backpack. Yeah, I know that's a ton of scratch for a tent, but Hilleberg tents are superbly made, light, and well-designed. They're more of an investment than a piece of camping gear.
For more tents to take you up, around, or near the world's high zones, check out Outside Online's Tents Buying Guide.