I'm sorry, that's plain incorrect. First, they're at Privet Drive, then the Burrow, then Grimmauld Place, then they camp for a few weeks-months but it's highly condensed plot-wise. They don't "run around the woods" at any point, that silly chase scene with the snatchers is onlyin the film.
Why do they hide? Because there is ZERO safe-space in the rest of the UK. They are forced into hiding to maintain their safety until such time as the horcruxes are gone and battle can commence. How is that much different from Frodo and Sam wandering the wilds alone at the last 2 LotR books? In HP, they are in society and non-wilderness far more than Frodo and Sam. And then they do a lot of epic shit at the end that has nothing to do with the woods.
Re-read the book, the woods part is a very small aspect.