Have done quite a bit of off road running, started with football training years ago. Great way to train, getting that fresh and clean air into the lungs and being out in open. Great sense of freedom. Sometimes it's good to be alone and just run.
Done all of these: Miles of fire trails (fire breaks) in SoCal which make excellent running paths. Can be steep to very , very steep on the same trail. These fire trails are on just about every hill to mountain top, so anyone doesn't have to travel far to use one. Excellent for stamina (endurance plus strength).
There are higher (one mile plus) elevation mountain paths/trails for loggers, forest rangers and old mining roads. The benefit of running in the mountains is that cardo is worked extra hard, until you get use to the thinner air. Lot of boxers train in the higher mountains lately. This is good for VO2 training, which tends to burn body fat at a more rapid rate. Notices, also, that athletes have better calves from hill/mountain running. Do what you think is best, but don't really need a backpack, with extra plates in it, if into serious higher elevation running.
For my friends in SoCal: Though very rare, there may be an occasion mountain lion or bear near some of these trails..so might pay attention to the surroundings. Coyote's are usually shy and stay away, if 3 or more, that's considered a pack...not a good sign. Some women runners will carry mace.
If lucky enough to live by a sandy area (ocean, river or sand dunes) take advantage of it. Super endurance builder and calf builder. And most all have hills to run up. Good Luck.