Then why would you play in a game set in Waterdeep?It depends on the city, I suppose. In the case of Waterdeep, for instance, I think the idea of a mad archmage's dungeon to be kind of stupid and I prefer to adventure in a location that's not chock full of epic level characters (so that my PC can feel like a big shot, not just some big shot's errand boy).
No, seriously. Leaving the city doesn't do jack, because your DM set the adventure in Waterdeep. You're basically just asking him to make shit up by leaving.
I agree that it's good to go off the rails to varying extents in most games, but not every GM is going to memorize or create a whole fucking world. Nor is every GM good at improvising. So if you just walk out of the area with all the quests, you should expect for nothing sensical to happen until the next session like 90% of the time. "I haven't thought about it" is a perfectly valid answer to a player question.
Seriously, if somebody wanted me to run a game where they could do literally anything they could think of in-character and expected me to do all the work of maintaining consistency within the setting and inventing all the NPCs and I had to run with it no matter how randomly off the beaten path it took them, they had better pay me fucking money. "Today I feel like traveling to the sea and looking for a boat to Xen'drik where I am going to start a bakery- What? Why would I care about the princess to whom I am betrothed being Gargamel's captive? Why are you looking at me that way?"
Sandbox games are a fuckton of work under the ye olde traditional DM model (a model I do not endorse but which many people are very attached too). I'm not running them unless people are going to be happy helping me invent new towns, locations, NPCs, plotlines, anything on the fly (and IME most people at least don't mind if not outright enjoying it). Basically, it won't look anything like normal D&D because I will demand players invent parts of the world. It will look silly, pasted together, and bizarre because collaborative storytelling will always be a bit less cogent. Because that way I can have fun too. But not every DM will joyously let players usurp part of the ye olde DM role. In most games I think you should expect to be on the tracks (totally locked in place) or on the interstate highways (there are branching paths and rest stops, but you still can't just get off anywhere) rather than off-roading.