I recommend staying in downtown Columbus so you can easily walk to restaurants, the Visitors Center where the architectural tours start and explore many of the great architectural highlights downtown. There are some very good options:
Hotel Indigo Columbus Architectural Center: I enjoyed staying at the Indigo which is a colorful, 85-room, contemporary hotel with mid-century modern touches in colors, furniture and artwork. It is located at 400 Brown St., on the western edge of downtown, across from Mill Race Park. The have a large parking lot with free parking as well. There is also a casual cafe/bar but I opted to eat in town to explore the several options there.
The Inn at Irwin Gardens: Set in a lovely, Italianate mansion built in 1864 by the Irwin family, the Inn has five traditionally furnished rooms and suites. It has lovely gardens which are well-worth the visit as they are open to the public with no charge, on Tuesday and Sundays from 2pm to 6pm from June through October. Private tours of the house and gardens are also available on the same days. It is located at 608 5th St., in the heart of downtown, and is a short walk to the Visitors Center.
Ruddick-Nugent House Bed & Breakfast: At 1210 16th St., this is Greek Revival home from 1884. It has four traditionally decorated rooms.