I go through a pair of tennis shoes about every 3 months and usually buy Nikes, but previously bought  a pair of Asics and liked them. The previous pair I bought ran true-to-size, so despite the warnings I ordered my usual size, which turned out to be really tight.  I used a pair of shoe stretchers and wear thin socks and they now fit perfectly.

I have several other more expensive tennis shoes, but these are now my favorites.