Try guild wars 2.
You can play without completly downloading it.
Its f2p and you can explore all together, since every starting map gets unlocked no matter what race you pick at the start.
It is also very easy to learn and you can even outlevel each other if anyone wanna keep playing in private, since you get levelcapped depending what map you are in.
Brilliant game design all around and still one of the best multiplayer games out there IMHO.
Guild wars 2 has so much variety i would not know where to start. Would just search it on youtube and find the fitting mood i guess.