Looking to go to the Caribbean islands need help with budget and experiences!

My fiancé and I are getting married in October and we’ve decided to go somewhere tropical. This has lead us to the islands. The one I’m specifically looking at is the grand cayman. Has anyone been there? Looking at hotel+flight costs I’m already at about 2k.

We will be staying Monday 10/5 to 10/12.

I’m wondering what all other expenses there will be? How much is food? Activities? Is there a better island? Neither of us have ever left the US. The most beach I’ve seen was Lake Michigan, she’s been to Florida several times.

Leaving from Indianapolis

Edit I should add that our budget is about 4K for everything. Willing to go a little more but would like to stay around there as our wedding is pricy already.