Recently downloaded the game, currently in Junktown. I solved the Gizmo quest with no difficulty, but I'm having trouble with two others.
First, the quest to bust the Skullz. I reached the point where they attack the bar-owner, I show up with the city guards, we kick their asses. Good and fine...but the quest doesn't complete. I show up at the hotel, kill the Skullz. Quest doesn't complete. Is it a bug, or am I missing something?
Second, the quest to save Sinthia. An online game guide tells me that this quest shows up if I spend the night at the hotel. But when I do, nothing happens. Again, bug? Or something I'm missing?

http://strategywiki.org/wiki/Fallout/Junktown Have a look here. There is a female gang member that sometimes slip away.

Hi, I've gotten quite adept with Fallout now after playing for a month or so. My advice is to go to the Hub after completing the three quests in Junktown and steal ammo/stimpacks from the guards wearing combat armor there, it takes awhile but you'll be set for the rest of the game if you do this (hopefully you tagged or put points toward steal otherwise it may take awhile). Also, feel free to pay Dr. Morbid a visit before leaving Junktown and use traps then lockpick on his locker in his basement for some nice goodies (having Katja is recommended for picking the lock since I doubt your lockpick is high enough that early in the game but changing the "game" difficulty in settings to easy also gives you a nice advantage since it just boosts your stats basically), then dispose of him and his guards for easy ammo and armor to sell (or equip, but I'm assuming you already have leather armor by now since you stopped the Skulz gang).

Lastly, did you recruit Tycho and Dogmeat from Junktown? They are the two best NPCs in the game and come in handy later in the game (especially Dogmeat!)