Know any co-op base building or exploring games?

Minecraft but if you've played starbound there's a good chance you have already tried Minecraft with them. It's probably the easiest game in the world and you can build anything you set your mind to if you haven't tried it with them yet.

I just played Portal Knights from this month HB bundle.

Terraria is very similar to Starbound, and worth checking out.

But if I may suggest something completely different:
Lara Croft and the Guardian of Light - This is a great co-op game, and a great gateway game. The action part requires twin-stick arcade shooter skills, but since it's co-op the stronger player can totally carry the team, and you can revive each other so that each player feels like they're contributing (and difficulty levels can be swapped at will). But what really makes it is that every puzzle (of which there are many, in every level) requires team-work. And the more challenging puzzles require solving before you can execute them, and the solving part is a totally gamer agnostic process where creative thinking triumphs and players can contribute regardless of gaming skill. It is perhaps the finest co-op game I've ever played, which scales well to gamers and non-gamers alike.

Raft
The Forest
Space Engineers
Medieval Engineers

There's Fortnite which has Save the World. Building, coop, defense like Orcs Must Die or Dungeon Defenders. Still have to pay for to access that mode.

sanctum 1 and 2 (i think... i don't played them, so not sure about it) --> tower defense

dungeon defenders --> again idk if you can make a party i don't played it, but it's online game so maybe........

however you want co-op in same PC or diferent PC with online multiplayer???

did you see astroneer? its new and still in early acess (booo). but I think it fits yours description.
I would recommend too sanctum 2 wich is a FPS tower defense.
last but not least you could try don't starve together, its really nice.
oh forgot one... its not really base building, but you cant get easier than this: stardew valley (there is co-op now)

Tropico 5 might be interesting to check out. If you're not afraid of going too deep into nostalgia, I can't overstate how many years I've spent playing custom maps in Warcraft 3 - I still do occasionally. Island Defense fits your description perfectly, although it requires more players than just two.

Fortified, a pretty neat tower defense game, with tps shooter mechanics. Best played in coop. Strategy plays a big part in it, so if you are into that this is ideal.