Hey there! I just moved to Manhattan last August for grad school. So far, I like it. It's a very quaint and friendly town.
Outdoors: Manhattan is lucky because it is in the most scenic part of the state (by far, in my opinion). The Flint Hills are really beautiful, especially in spring and early summer when they turn vibrantly green. There is an area outside of town that is a sort of nature preserve/research area run by K-State and the Nature Conservancy called the Konza Prairie. It is a stunningly beautiful hike with several loops of varying lengths. There are also two massive lakes right outside of town (Tuttle Creek and Milford), and boating is apparently popular there. There are some other nature areas near town, but I haven't checked them out yet.
Cost: Yes, Manhattan is very expensive, by Kansas standards. The town is growing faster than they can keep up with which results in a housing shortage and high real estate prices. You might try looking to the east of Manhattan, just outside of town there are some more affordable options.
Overall, Manhattan is a really nice place. Like someone else said, there are really no bad areas, and the whole community seems pleasant. It is a tad rural for my tastes. Jacked up pickups are the norm, which can get annoying (to me). But there is a good mix of people. Aggieville is where all the undergrads go to get wasted on the weekends, but there are some decent places there. Downtown also has some more upscale establishments. Hope this helps!