Looking for tips for a honeymoon in either mexico or virgin/Caribbean

I have never been to any of these locations so looking for any advice you can give.

We would prefer a more DIY adventurous trip over a relaxing all inclusive resort kind of thing. We'd like to go for about 5 days and have a budget of ~$3k (kind of adjustable if its really worth it). Right now we're looking at Tulum but would love other suggestions/info about logistics that I'm not thinking of. Thanks in advance!