I prefer to stay at the Hilton College Station & Conference Center because it's clean and updated. There is no microwave or fridge in the rooms, but the bar will fill up your cooler for free. There are nice grassy areas to walk your dog. It's a bit pricey, so having a roommate helps.
The other place to stay without paying a pet fee is the La Quinta. I don't like it as much because it's run down and there are a lot of vicious dogs in the backyards of the homes facing the parking lot. There is no microwave or fridge in the rooms either. Some clubs offer a discount, so check the premiums.
The La Quinta in Belton is really nice and within walking distance of the Bell County Expo Center. The only drawback is that it's miles from most restaurants, grocery, and Starbucks. There is a taco place in the gas station across the street and a steak house in the parking lot, but it's not open on Sundays.