Hi.
If you'll look in thrift shops, you'll save a lot of money and find obscure games that are nonetheless fun. They get discarded after someone dies or the kids grow up. Sometimes they are entirely unused.
Uno gets a little tedious with just two players. It needs the chaos of a group of four or more to be much fun.
Try Pente. It was the rage back in the 70's, but is still a great game. It uses a couple of simple premises to work, but it's great for two. It comes in cardboard tube or in a regular box. It is visually appealing plus it allows actual strategy.
Another great game that works for just two is Othello. It also involves strategy, but isn't so involved as chess, so it allows for conversation, a movie in the background, children present, or other distractions in the room.
Mastermind is a good game for two. It is as varied as the players. It works like Battleship, but with colored pegs arranged in order instead of battleship around a sea.
And finally, if you like words, either Upwords or Boggle are great for two.