I give all my clients the following advice no matter where they're looking to buy :
take a walk in the neighborhood before making a decision to purchase the home/investment property they like.
You're in the U.K, take a flight to Chicago, spend a weekend and make up your mind after you've had a chance to do more research. Also, as an Investor you need to take into consideration the tax implications of owning a property in the U.S as an Investment (income tax on rents, property taxes, Foreign Investor Real Property Tax Act-FIRPTA) and will be required to obtain a Taxpayer Identification Number-T.I.N.
Good Luck, Ken Dooley.