I wouldn't get a Hyundai Sonata within your budget. The 2011 and 2012 Sonatas were unreliable. The ones before that were when Hyundai wasn't great.
A 2009 or 2010 Accord would be nice. Has a huge back seat, it's comfortable, roomy, smooth, and handles well. Like most Hondas of this time, road noise was a problem. Gas mileage was only 24 for the 4 cylinder and 22 for the V6.
The 2008-2010 Camry may be the best option. It's one of the most reliable cars on the road. 2010 brought a more fuel efficient 6 speed automatic. It rides more softly than other midsize sedans and is one of the quietest. MPG is 25 for 2007 through 2009 and 26 for 2010 and 2011. I'd suggest the hybrid, which is also faster than the 4 cylinder. The Hybrid gets 34 MPG. The Camry has the third lowest maintenance costs of any car. It isn't an exciting (actually it's very boring) car, but it is a good car.
If you want even more mileage you can get a Prius. My 2005 Prius gets around 40 MPG and my 2016 gets 55 MPG. The 2004-2009 Prius is very roomy, bigger than it looks on the outside. You could definitely get two car seats in the back, but not two car seats PLUS adult in the middle. The front seats are roomy so you could always scoot the front seats forward and still have room to spare. The Prius has the lowest maintenance costs of any car.
You could also check out a Kia Soul. Very practical, second lowest maintenance costs of any car, and has depreciated a lot. It isn't nearly as comfortable as the three other cars I mentioned though.
All these cars have good safety ratings. Good luck with your purchase!