The Mountains are located to the west of the farm. On the way to the village you'll pass the entrance before you continue west. There is even a little sign telling you in what direction the village and Mountains are. The Mountains are also the only place where you can get a constant supply of Wood for fencing and building material. The tree stumps will become 6 wood when they are chopped up using the ax. If you leave the Mountains and come back, the tree stumps will "regrow" mysteriously and you can chop them up again.
There isn't much excitement going on in the Mountains. It is a peaceful little place away from the hard work on the farm and the bustle of the village. The only animals around are the insects, rabbits, squirrels, and foxes that show up on your screen from time to time. To see the wild animals, just stand in the woods for a while. They'll eventually run across your screen.
The Insects differ from season to season. In the Spring, butterflies and ladybugs (along with the occasional dragonfly) will appear. Summertime has a lot of beetles, dragonflies, and lightning bugs. Each bug can be caught using the Bug Net (buy from Bill for 500G) and is categorized in the Bug Book at the Library. For more information about bug collecting check out the Library Guide. Some bugs will appear only during the day and some will appear only at night.
The Hot Springs are now located here instead of being underneath the Tool Shed like in Harvest Moon 1 for Gameboy. The Hot Springs helps you replenish energy when you're weak from hard work. It doesn't replenish you fully, but it helps when you're really weak and can't make it to town to Rosie's Restaurant to buy food. The Hot Springs are in the upper northwest corner of the Mountains. To use the Hot Springs, stand on the wood platform and press the A BUTTON. Your farmer will strip down (oh la la) and jump into the water. When you want to get out, just head back to the platform and press the A BUTTON again. As far as I can tell, sitting in the Hot Springs for long periods of time to replenish your energy is no different then just jumping in and jumping back out.
The existence of the Mountains means that you can always have something to sell. Depending on the season, different items will appear under the trees. There are three total, and you can pick them and drop them off in the shipping bin. They'll regrow every day except for in the Winter when nothing grows. Two of them are located close to the entrance to the Mountains. The third is located up north by the Hot Springs.
There are two exits back to the farm. One is of course the same way you walked into the Mountains. The other is located just right of the Hot Springs. Right by where the boy is standing in this screen shot is the second exit. Run into the trees and you will end up right next to your house back on the farm. It makes picking that last berry/cherry/mushroom easier since you don't have to run all the way back through the woods and then back to the farm to drop it off in the shipping bin.