Hey gigi, I personally use HitBTC, cryptopia, and KuCoin. KuCoin is an up and coming star very similar to Binance. All of these have smaller altcoins and the majors supported. The only real issue with them, is sometimes you don't have the volume being traded on these exchanges at the same levels that you do on the ones you mentioned. However, that usually is a coin by coin basis.

Happy Hunting. Update me with where you go!