How do you go about identifying the area to buy?

But, we would only have 45 days to identify a new property.

The most important area to identify is whether or not you have a deal at hand.

The best place to start is identifying what your long term goals for investing look like and work backwards from there.

The Starbucks and Whole Foods theory isn't a distance to theory really, it's more of an upswinging neighborhood identifier.

My property suppose to close the first week of June and I would need to identify properties within 45 days then purchase them within 180 days.

There's a bunch of ways to put your puzzle together that may benefit you.Like @Bill Brandt said, 45 days to identify and 180 days to close. 

If you can identify a transitional C to B- (not war zone) pocket in a high payment standard zip code than you can sometimes get more rent from section 8 than you would normally on the open market for that zone.

For the Limited 203k, even though a HUD approved FHA 203k Consultant is not required, you'll still want to use one to ensure that all FHA MPS/MPR items are identified prior to getting pricing from any contractor. 

Once you identify them, reach out to them and see if they are a good fit.