Mountains might seem as an obvious place to go, but think carefully; a lot of trouble waits in high places. When you’re king of the hill, you can see everything, but almost anything can see you. Everyone knows where the king is, right? Depending on the mountain/hill in question, camouflage could be a problem or a gift from nature.
Some hills and mountains are filled with trees which will provide you with camouflage, building material, fire wood, trap and weapon resources and birds and other small animals which you can eat, after cooking of course ;).
Also, a lot of mountains are riddled with caves and nooks, which you can use both for protection and for storing your equipment. But be extremely careful; no matter who attacks you, while in a cave, you’re in a pickle. You only have one exit, which the zombies will flood if ever finding out about you. Human marauders/bandits/robbers/gangs and such will use smoke and fire to flush you out. If you’re not hiding properly in the mountains, someone will eventually come. Zombies, evil humans or survivors having the same idea as you.
Extremely steep mountains with no vegetation are perfect for defending against zombies. They are also perfect for killing humans. No vegetation means no food and not enough water. Sure, you’ll find pools of water, but you’ll have to boil it to make it safe to drink; fire makes smoke.. and a lot of smoke means you’ll soon be in trouble.
If you fall or otherwise injure yourself, no simple med kit will save you. It’s quite easy to brake your leg or arm… and then eventually die; you can’t call for help ’cause you’ll attract the undesirables and there aren’t any rescue teams out there with helicopters and ropes waiting. If considering one of these mountains, you better be sure there’s a military base hidden somewhere up there or you know the mountain in question your entire life. Never go to very high mountain tops! If the cold doesn’t kill you, the lack of food will, and if that doesn’t kill you, the extremely harsh winds will kill you. Ice glaciars are, of course, out of the question.
Getting water in “normal” mountains and hills shouldn’t be a problem if you know how to build a solar well or “pump out” the water from tree branches using plastic bags. However, doing this for one person is easy, but for an entire group it’s almost impossible. You’ll need to find streams since building a well in a mountain is next to impossible and in the long run maybe even harder to do than in the desert.
Hills and mountains with vegetation usually aren’t that steep and therefore do not provide with enough protection against zombies. They’ll eventually climb up there, slower of course, but they still will. Large mammals don’t stay in the high ground for too long and tend to be in valley where it is more easier to find water.
Imagine the following. You have a completely safe compound somewhere on a mountain. No one can see you, hear you or even smell you. It’s all good in the beginning. But soon the water supply runs low; now every few days you have to go down and climb all the way back with liters and liters of water on your back (remember, near your base, you’re already using solar wells and plants for water). After a few months your food supply runs low, and as all the highlanders had to do.. you go down the hill to find food. If the mountain doesn’t kill you the strain of walking up and down will. In the desert you’ll at least have a few hours a day to just sit back and think. Even in this situation you should always avoid the peaks.
If you know a certain mountain very well and know of places you can use to fortify and hide (hidden cabins, rescue stations..) or even find water (some mountains even have lakes and caves with large pools of water), then by all means, run to the hills! If not, you’re better off someplace else.