Definitely the Chief campground, by far. The vibe is usually great, and you can meet partners if needed. And theres the always fun drunken 10pm bouldering. If you need a shower the rec centre has $2 deals at noonish on weekdays.
Crowds in June aren't too bad except weekends, and really only on 5.10 or less routes. The lower the grade, the more climbers you will find. I find the best strategy to avoid lineups is to start really late, mainly because I'm lazy and slow people will always get up earlier than me.
Joffre and Matier are a lot of fun, and you get to start high. Not sure of conditions.
Skaha is rarely wet in June, unlike Squamish. It's probably your best bet.
Unlike some of the other posters, I would avoid Ultimate Everthing/Diedre/Calculus unless 5.8/9 is your limit. These are by far the most crowded climbs you will find. In the 5.10 range off the top of my head I would try Angels Crest, Sunblessed, all the cracks at the grand wall base, Great Game, and Centrefold. Maybe a day at the smoke bluffs. At 10+/11- add Milk Road and the Grand Wall. All of these routes are well protected (except the first few metres of sunblessed) and IMO are of excellent quality. Probably the only one to worry about crowds is Angels Crest. Avoid the weekend for it and you're fine, or start at noon.