Simple changes that go a long way:
Living Room:
- Paint the walls a warm, neutral colour to brighten the space
- Change old light bulbs to warmer, softer ones for a cozier feel
- Add a small accent rug in a complementing colour to bring some texture
- Recovery cushions or add new colourful throw pillows.
Kitchen:
- Fresh coat of paint, perhaps a lighter colour to brighten the space
- Update old cabinet handles and knobs - inexpensive but makes a difference
- Add some potted plants on the window sill or small hanging plants
- New appliances in complementary colours can bring a modern feel.
Other general ideas:
- Pressure wash paths/driveway to freshen up the entrance
- New doormat and a nice pot of flowers by the front door
- Curtains/blinds for any rooms that need them
$2000 won't go super far, but these small changes will definitely make the place feel refreshed and homely.