Sorry for the delayed response. I turned in my dissertation this week, so it was a little stressful. Let me address your questoins:
Lafayette and West Lafayette and the surrounding areas make up a relatively small areal I wouldn't worry too much about the exact location unless you want to rely on public transportation. The buses are free for studenst which is awesome. You will probably want to live somewhere with no bus transfer. If you live far enough away to need a bus transfer, you might as well just drive. Driving to campus is easy enough. A parking pass is something like $250 for a gravel lot pass which is what you will be eligible for your first year. After that, you can pay a little more for a garage pass which is really nice.
West Lafayette Housing: Most of my friends live in apartments in West Lafayette. there are some apartments that are primarily undergrads. You will likely be able to tell which ones those are by the price, amenitites, etc. If it's luxurious, has the word "lodge" in the title, or has a "parent's page" on their website, you probably don't want to live there. Willowbrook, Blackbird Farms, and Salem Court House are probably some of the best places for grad students. There are certainly others, but I have known peple in all of those places. The aparetments are nice, public transportation is easy, and you could bike to campus from all of these. Willowbrook and Blackbird Farms are really close to the trail system which is really nice for running and biking.
Lafayette Housing:
DOWNTOWN: I grew up down town in Lafayette. There are more and more apartments popping up in old houses and old buildings. Most of these would have character and have potential to be less safe if you pick the wrong street. Generally streets north of Ferry Street would not be very desirable. There are some streets south of South Street that are a little iffy, but you will probably be fine. Just don't be stupid. Most people I know who have apartments right around Main Street LOVE it. There is a bus called the trolly that goes between down town and campus every 15 minutes. There are several bars and cute restaurants down town, a farmers market all summer and fall, and other little events here and there. You will want to ask about parking for these apartments. Most have a spot, but the street parking is usually 2 hour parking from 7am to 5pm, so it could be a pain for visitors.
SOUTH SIDE: The south side of Lafayette revolves around Veteran's Memorial Parkway. It's practically another city. Not in distance though. It's literally a 12 minute drive to campus from the furthest apartments in this area. Everything is going to be around 5 years old or less, becuase it's all new development. Ther'es a Super Wal-Mart, several restaurants, nice big apartments, etc. I would actually highly recommend this area. It's going to be cheaper and more quiet. It would requier a car, but the money you save can be applied to your parking pass etc. There are a lot of cheap houses as well. If you are in a position to buy a house, you can find a cheap one becuase sadly...a lot in that area are up for quick sale. They are nice houses in nice neighborhoods. It's just a product of the time when a lot of young people got in over their heads financially. I have 2 friends who just bought houses becuase it was better for their family, dogs, etc and mortgage payments were cheaper than rent in some areas. This is also a good area if you have a significant other who wants to work in Indianapolis while you go to school at Purdue.
CAMPUS HOUSING
I haven't had any friends who live right on campus. At least not for more than a year. There are some nice new apartments going up, but they are of the variety with "parent pages" on the website. If you want to experience the whop whop whop sound of helicopter parents, go for it. The main bars are close to these apartments, so you will have the roudy crowd close by. If you're going to work in a lab, and experiements need tending on a Saturday morning, this is not the area for you. Chauncy Hill is the area I'm talking about. Grad housing on campus is less than idea. Hawkins is a dorm. It looks like a dorm, and feels like a dorm. There are shared kitchen spaces, but you won't get a kitchen of your own. You also have to share bathrooms. For the price of apartments in the area, it seems silly to live in Hawkins to me. Purdue Village is not ideal either. A lot of international students like living there because of the community they have developed. The chinese students developed a thriving garden which was awesome! Often there is room for families to live together. The facilities are not that nice though. Cinderblock buildings with small bedrooms and ok kitchens. It's Still a 15-20 minute walk to most areas on campus. I had a friend from China who really liked living in Purdue VIllage her first year. It was her first time to live far away from home, and she appreciated the community there. She moved to an apartment of her own for her second year. I think you can find cheaper apartments with more ammenities though in other areas of town.
I have never felt like the Greater Lafayette area was in the middle of no where. Lafayette is an easy 1 hour 15 minute drive from Indianapolis (1.5 hours to the airport) and about 2.5 hours from Chicago. I love being between the 2! You can do either as a day trip. My friends and I have driven to Chicago just to go out to dinner. We have cultural events down town as well as on campus. The public libraries are fantastic. Winters are unpredicable. Often very cold, but not Minnesota cold. Summers are hot and humid. You're going to be working 95% of the time anyway, so I wouldn't get too worked up about the social scene. We have one. It may not be the same scene as other places, but we have one.
Any more questions, just give me a shout!