I have worked the Mendham and surrounding areas of Morris/Somerset counties for 10 years now and know them well. Yours is a tall order in our area. Although prices there have significantly softened, $300K in Mendham will not get you into a 4 bedroom house. Chester and Long Valley have offered some good bargains in that range this year, but our markets are tightening a bit with lower inventory, so its hard to say if this Spring will be as generous.
I find that most people can realistically expect to get about 75% of their wish - no matter what their price range - so I suggest you start by creating a list of your needs vs. your wants. Prioritize your wish list before you choose a town. If the price is firm, that's your first priority and the town becomes second or third on the list. If the sky's the limit, then town may come first. Do you have children in the school system, or is that a future need? Pools here in NJ are useful for only about 3-4 months a year, so you may be better off to choose a town with a nice town pool - Chester, Bernardsville, Succasunna aka Roxbury Twp - come to mind immediately. How about property? Would you rather have more play space in the backyard, or that pool? You get my drift...
If you are serious about looking, start by finding a Realtor to help you properly define your needs and match you to the towns that can offer you the best choices. It will help you avoid a lot of wasted time and frustration.