Open world games have always been a bit of a challenge to keep players entertained for extended periods of time. Grand Theft Auto is a great example of a game franchise that has effectively developed a fun openw orld environment that can keep people interested and returning for more. However, I'm not too sure on how I should go about this in an open world zombie survival style game. I know NPCs should(and will) give quests, but I want to know what kind of mechanics, quests, and features that should be implemented to maintain player interest in a large-scale multiplayer environment.

Grand Theft Auto kept peoples' interest because it was so over the top ridiculous, just like Saint's Row.

Maintaining interest in a multiplayer environment should involve competition or having the players build something that requires them to maintain it. Mainly you should just ensure that players feel like they're having some sort of impact on the world, instead of just collecting zombie-hides for quests. The competition aspect can be pretty simple, formation of gangs to control territory against the zombie hordes will cause players to band together and make them less likely to abandon your game and thus abandon their friends. Fortification and upgrading of buildings that slowly fall into disrepair also can aide your gang in holding back the undead tide while also making you feel like the effect you have on this world is important. Requiring player participation to build economies can also have this effect.

Ultimately you want your players to come together(although not necessarily all in one group or you kill competition) and feel like they're needed in your game so that they keep coming back for more.
I agree entirely with BrickSquadron. Competition is a huge factor in the success of countless games. I also believe an idea you should consider toying around with is hiding. There are bound to be times where the hordes of zombies have overwhelmed a building and trapped you in horrible odds, so why not make it possible to use various things around you to hide and try to evade them until someone can hopefully help you out?

Making it so you can interact with a lot of things around you is another big plus to open world games, in my opinion. It doesn't make you feel like you impact the world, but it does make you feel more like you're a part of it.

Also, world events. I cannot stress enough the importance of these. For example, you could have an event occasionally occur where there is an area of some sort that needs to be secured, and the players must team up with some and struggle against others to try to secure and protect an area for valuable resources it holds. Not the best example, but you get the idea. Events can be very exciting, especially since they get most players involved whether they're friends or foes, and the outcomes of them should be unpredictable.
there are 3 things that kill open world games

lack of content(not enough things to do/empty space)
lack of direction(not knowing what to do/where to go)
lack of consistency(unevenly spread content/atmosphere)

If you want to look at a good open world zombie game (its browser base mostly text) that keep a lot of people busy try - it has a lot of content you may be able to incorporate them.

Especially the part where you can barricade yourself in a house / place you have to maintain the barricade as it deteriorates over time from attacks...
i think a zombie mmorpg should be based around the colonies and such players form and the struggle to survive. there are too many zombie games that encourage ramboing or aggressive violence over patient strategy and actual challenge beyond how much damage you take from zombie attacks.

urbandead is pretty boring, to be frank, and it doesn't do a good job of providing consistent and interesting challenges to successfully survive.
In response to .procyon-444
Personal opinion.
Open world games need to have interesting worlds and it's hard to make a 2D top-down tile-based world interesting. I think it could be interesting to need to find ways to adapt to the environment to survive, but 3D environments can be so much more intricate that 2D maps just lack the same possibilities.