Lillym, without knowing where you are travelling to, I can't offer much in terms of specific places to stay. But here are some guidelines:
First of all, there are specific companies that specialize in longer visits, such as Residence Inn Mariott www.marriott.com/residence-inn/travel.mi Extended Stay America www.extendedstayamerica.com and Studio 6 www.staystudio6.com
Not all companies are available in all locations, and some are more "posh" than others.
These are different from companies that are willing to quote you room prices for longer stays (by the week) such as Motel 6 or Holiday Inn or LaQuinta. An extended stay company will typically offer rooms that have a kitchenette (microwave, larger fridge, sink, stove) and also have laundry services. Because their guests are staying long term, they are also less likely to have problems with cleanliness - they aren't turning over the room quickly, where issues might go unnoticed or unaddressed.
There are many places you can go to get reviews on particular chains, as well as individual locations. Try Travelocity, Expedia, TripAdvisor, etc.
My suggestion, if you are going to go the "motel" route, is to spend as much as you can afford. I travel a lot for dog shows out of state, and have stopped using Motel 6, Red Roof Inn, etc. Any of the motels that are under $50-60/night. Not that these are bad companies, but as a single woman traveling, the lower the price-point, the more likely the clientele will be undesirable. I stick with LaQuinta (they have a rewards program, & no pet fees, and include a continental breakfast daily), it's affordable enough, & they will offer discounts on longer stays.
There are also corporate rentals, which provide furnished homes, apartments and hotel settings for short-term and long-term stays. One example is www.corporatehousing.com
These companies can be pricier, as they often work directly with companies, who can afford to pay more than someone footing their own bill for travel. But their reputation is at stake, and the locations that you stay at through them will be vetted & more likely to be free of problems.
If you are paying for this yourself, obviously price is going to be of some concern. Your best course of action is to find the best place you can afford, and stretch your budget as much as possible. For 8 weeks, you don't want to be miserable! T.