From Wikipedia, Wayne Manor is depicted in earlier comics as being on the outskirts of Gotham City in the state of New Jersey. Comic book portrayals place the mansion within driving distance of Gotham City, close enough that the batsignal can be seen from Wayne Manor alerting Batman of distress in the city.
Well, we don't really know why he didn't raid Wayne Manor. Some possibilities would be:
- Miranda's Dad burnt down the place, so any old stuff at Wayne Manor is already destroyed anyway. Any new stuff may not be of much interest or value to people planning to end their lives in an exploding city.
- Bane had already captured Bruce and would not have expected a batcave under Wayne Manor because he'd have assumed the armoury in the city was Batman's storage area.
- The building is on the outskirts. Bane's primary work managing a lot of unruly people, is in the city. Yes, he could have visited Wayne Manor, but for a commander of his calibre, rummaging through somebody's house may not have been as much "fun" as breaking a plane into two or raiding a stock market or freeing prisoners. He could have sent someone to do the rummaging, but what would he get out of it? He didn't even find Bruce's other hideout in the city (where Bruce conducts experiments on bullet shattering). Bane has a larger plan: to destroy the city within a limited amount of time and before the patience of his people run out (remember his man in the broken plane asking if his sacrificing his life won't go in vain?). So Bane can't afford to waste time in side-quests.