You can have random encounters in the worldmap, but you have to trigger them yourself. They won't automatically appear when you travel.
You can do a few quest but you will run short of unique quest pretty quick and the repeatable quest will eventually disapear.
The most challenging activities are PVP (for control of the zones) and dungeons (usually 2nd floor or undergroup, on many map). Both most likely need team mate, especially if you don't have experience with the game. Even after that, most will still require some team mates.
Although, you can still wander in the city, scavenge, fight npc, explore etc... It can be interesting when you don't know the gameworld yet, and when you need to level up a character, but after you have seen everything, fought every npc and got every levels, or even before that, it will get boring. Also beware when you explore zones that aren't owned by your faction. It will alert your enemies.
As it is now, you better join a team, considering you won't see any other scavengers and PVE players. You would if we were more numerous and if the core was more dynamic, but currently, only an handfull of PVP players are still on the game.
But at the same time, joining a team is much much easier than other servers. You just need to join a faction at the beginning, and then use faction chat ("f/") to reach the other members of your faction. Currently, only VTEC and lawyers are fairly populated, mostly at dayfall/evening european time.