As long as you're not bringing the cats with you, you can have several options in Inverness. There are several Premier Inns in Inverness; the farther away you are from the city center, the less expensive they are. We've stayed at the Premier Inn near Raigmore Hospital. It's clean and comfortable; there is a restaurant on site; and there's a 24 hour Tesco within walking distance. Plus you can catch the bus in to town very easily. There is another Premier Inn on Nessbank, next to the Ness Bridge. There are two other Premier Inns in Inverness; one on Millburn Road, on the way in to town; and the other on the western outskirts of town.
Travelodge is another possibility. We recently stayed at the Travelodge Inverness Fairways. It was much better than we remembered. In 30 nights of staying in hotels, B&Bs and hostels during the summer, the Travelodge was the only place we stayed that provided a fan in the room. There is a Travelodge closer to town, and also one closer to the airport. Even though we stayed at the Travelodge in mid-July, the cost was surprisingly cheap, compared to other lodging in Inverness.
Best thing to do would be to check the reviews on TripAdvisor, then compare prices.