Center room of the house. The center of a building is usually the strongest point; or, a stairwell. I know all of this, because we get a minor tornado in the area about once a year, and I always worry, as we have no basement!
If there's no basement, nor a stairwell, get in a room with no or the fewest windows, or a sturdy closet, OR face-down in a bathtub, covering your head neck, and back with your arms and preferably something like a mattress. If possible, be on the first floor.
In my house, I'd try to get into the small, walk-in pantry under the stairs--I'm short enough. Trying to get 7 cats and a large man in there may be a tad problematic, though! The other option is the stairwell or the foyer.
If we're dealing with a hurricane, to which most of the above applies (until the flooding starts, then you want to get as high up as you can), we'd camp out in the foyer. It has no windows, apart from a tiny safety glass one in the front door. I'd remove the chest of drawers and the chair, so they won't become airborne missiles. I'd also bring in sleeping bags, jugs of water, food, blankets, cat food and bowls, and enough water for them, and a litter box or 2, a battery-powered radio, flashlights (NO CANDLES, please!), extra batteries for the former, and something to read, a game, etc. to pass the time. If you can bring in a land-line phone (NOT cordless), that would be great. You could be there for literally hours. Also be prepared to move your stuff quickly to a higher floor after the wind stops.
We're not very close to the coast, but we would get a lot of the hurricane here. We've had very wild, hurricane-like rain and winds a few summers ago, and 81,000 residents lost power for almost 2 weeks (we were very lucky--we only lost the phone, cable, and Internet for about 12 hours). They lost power at work, and we had 3 days off. I've lived in this area all my life, and never remember all of this happening on such a scale. the only other time work closed for more than 1 day (for weather) was the winter of '94-'95. The Governor wanted all non-essential state and county offices to close for 5 days in order to save energy. The coal needed to fire the electric plants couldn't get in, due to the ice and snow (we had 17 storms from December-March).
Great weather survival tips: www.noaa.org