Just got a Switch - what games would be worth looking into?

[Evil Yoshi Toes]

I haven't played the second Splatoon, but if you're looking to play with your girlfriend I'd say Mario Kart. I like Splatoon on the Wii U, but the local multiplayer isn't all that engaging. I'm not sure if it's better in the second game or if it is even present, but judging by what Zero Kirby said it seems Mario Kart is the better option for local multiplayer.
If you're a Zelda fan, Breath of the Wild is pretty good. I'm also looking to pick up Tropical Freeze eventually; it looks like a lot of fun!