Fun game, brain dead easy interface to learn, fast turns, simple as hell multi player environment. The game is a well developed well supported design and there is numerous expansions to indulge.
Panzer Corps, same comments as above, but it is operational level style.
This games are not overly detailed complex mega game tedium though. Just ignore the inevitable 'beer and pretzels' remarks. I enjoy beer and pretzels while playing any game, so the remark means virtually nothing.
Now if you want a very nice game at the grand strategy level, probably one of the best choices is Strategic Command. It's not a new game, you can likely buy it for peanuts, but it is still one of the best games to get your fix of more conventional board game wargame looking experiences.
I am mentioning these designs all specifically for their play a turn, send a turn aspects.
You might also look into Combat Mission. It is turn based as well.