Finding a phone which works in any particular location from one of the carriers is always trial and error. Throw in the various building/construction types and it becomes extremely variable, even within a specific neighborhood. There are some strong contenders though, such as your RAZR, and some of the very basic Nokia candybar style phones, which are obviously not as popular given the arrival of the smartphone/iPhone trend of late. The one advantage of *not* going with one of the 'free' phones from the carrier is that you likely have a better chance at finding something which works in the long run. YMMV. Location is everything though. If you live too much in a fringe area, or in an area where 3G service ends, sometimes the phone bouncing between networks can present problems holding/receiving a call.
Have you gone online recently and checked the online coverage map @ ATT? It would be helpful to know your zip code to take a quick peek at which carriers service your location better than others in the case where you though you might have to switch.
FWIW, I've never had good luck with LG GSM based handsets. GSM/UMTS is the technology ATT & T-Mobiles uses by the way. The LG CDMA handsets for Sprint, Verizon, etc are a bit better RF-wise. You could try picking up a newer RAZR from Craig's list or ebay instead of going with an ATT issued phone per se. Or are you limiting yourself to what ATT offers on their web site or corporate stores?
The other option you might consider is to install a repeater/amplifier to provide coverage for your entire home, or maybe just a room/office/etc. That can be a little pricey depndinig on which equipment you require (antennas on the roof, for example), but if you need to stay with a particular carrier, it may certainly be useful.
What other handsets have you tried, and are you mainly having issues using your phone *inside* rather than just outside your front door/yard(?)
I am about to get a new cell phone. I am not concerned about aps, web surfing or anything other than making / receiving calls and text messages. I live in a rural area with spotty coverage. I will be using AT&T as my service provider. My main concern is signal strength. I had a Motorola Razor a few years back and the signal was great. The past two years I've had an LG and the signal has been horrible. What suggestions for a new phone that will suit my needs? Is there any code or identity on each phone that would indicate signal strength?