You definitely won't have to worry about snow in late August unless there is a freak snowstorm (which has happened in the past). If you want to avoid crowds stay away from Logan Pass. Getting there early is a must to find a parking place and you will avoid people on the way up...but on the way down you will have to contend with thousands of gawking tourists (maybe a slight exaggeration) on the only trail back to the Logan Pass parking lot (not fun, I've done it more than once).
Pollock is a good choice as you park at Lunch Creek and you also have the option of doing Piegan from the Piegan-Pollock saddle, if you think you have enough time...both of those are worthwhile peaks. There is still road construction going on in the park on GTTS Road.
If you want to avoid people and road construction head to the SE portion of the park. Calf Robe is a good option there. Lots of bears...make sure you carry bear spray. Two Medicine gives you lots of options....Bison Mountain, Medicine Peak, Appistoki Peak will all give you magnificent views...Appistoki being the longest and hardest of the three.
Stay off the Highline Trail unless its on your bucket list....usually filled with rude "hikers" who know nothing about trail etiquette.