I'll be travelling to Moscow and Saint Petersburg in July. While searching homes, I noticed that most homes do not have air conditioning. How livable is it in these cities without A/C?
People used to live in the tropics and subtropics without air conditioning - and indeed, many still do - so it's livable. It's all about what you can tolerate.
Also, where you normally live is going to affect the answer. From Miami or Bangkok? A hot day in St. Petersburg is going to seem fine. From Tuktoyaktuk? Maybe it will be pretty intolerable.
St. Petersburg's record high temperature - of all time - is only 37.1 degrees (98.8 F) and Moscow's, 38.2 degrees (100.8 F). Moscow's normal July high - the hottest month - is 24.3 (75.7) and St. Petersburg's, 23.0 (73.4) - so in normal weather, air conditioning will not be required. During a heat wave, yes, you'll probably want it but you'll probably find such times are brief and reasonably uncommon. (All these statistics are from Wikipedia's climate section of the respective city pages.)
If you find that you can't tolerate such temperatures, travel during the shoulder season. By early September (which is still summertime, astronomically), daytime highs have cooled to an average of the mid-teens (high 50s/low 60s F) and the heat waves should be much rarer indeed.