This may not be something fun to DO for your anniversary, but it's something I wish we had done on every anniversary.
Get a professional portrait done of the two of you. It doesn't have to be all formal in a suit in the studio. You can have one taken outdoors at sunset, or while you're on the beach, or whatever. But as one who has been married for more than 40 years now, I can tell you it's one thing I really regret not having done. Years from now, looking back, those memories will be priceless, especially if the pictures are well-made by a pro.
B4ed and breakfast weekend getway.
How about going to a nice spa? Get massages together or wraps. Sometimes these places have couple packages.
The traditional gift for the one year anniversary is something paper. Now,I'm usually not one for these traditions but my darling husband went out and bought me some tickets to a show I have been wanting to see for ages and I thought it was a great anniversary present.