Since it is a wedding anniversary I would choose to spend the budget on a joint present - and if possible that would be a holiday for the two of us.
My husband and I are longing for the day we can travel alone again however since we have 3 teens, one with a sporting commitment that keeps he and my husband travelling regularly plus a business to run and parents getting older that seems a bit of a pipe dream at present.
Upgraded to a 1.81ct solitaire at 10 years, but upgraded again to 2.80ct at 20 years . Turned my 1.81 solitaire into a 3-stone!
Paris was very romantic. We left the kids with my parents for a week, and went to all the must-visit sites like the Louvre, Versailles, Notre Dame, Sacre Coeur, and had our anniversary lunch on the Eiffel Tower ( Jules Verne).
I think you should both independently write a bucket list, and then come back and compare and write a joint one.
Pick something you both agree would be amazing (something you've always wanted to learn or be able to do; or some experience/place you've always wanted to visit). Congratulations on 10 years of marriage, that's really something to celebrate.
Our best $10K was a trip to London (from the US) with our middle-school-aged kids -- our first international trip with kids and our first as a couple in a long while. Most of the cost was airfare, of course. There was a lot of what my kids would now call "Type 2 Fun" -- hilarious memories of at-the-time stressful or baffling ordeals ("OMG, remember ______ !"). As long as we kept our cool, we knew it would be fine -- and spouse and I had to keep reminding each other along the way .
I love gems -- and these memories are better than any gem.