Jake already suggested Cuba but I personally think the Dominican Republic is the better option in the Caribbean. I haven't been personally even though I had the chance but friends of mine went there and said they had a blast. The beaches are great they said and it was really cheap. Given that they booked from the US but still it should be considerably cheaper than anything in the Indian Ocean in my opinion. I also think culturally it is much more interesting to explore than the Indian and you are less likely to get bored.
I have friends who went to Bally and they were very disappointed. If you are decided to go to the Indian my suggestion is to go to Bora Bora as I have heard positive reviews.
If you are not adamant on going to a golden sands beachy island and if you are up for some exploring, an unpopular suggestion I can make is Chatham, Massachusetts. I have lived there for a little while and it is a cosy, kind of secluded place that hosts a lot of weddings so has a romantic vibe around it. The beaches aren't spectacular and it will be kind of boring probably but feels right for a honeymoon as I imagine you are not aiming at partying. You can take a boat and do some whale-watching in the region of Nantucket and if you are lucky you might spot a great white as they are common around there. The cuisine is also nice and I can tip you some great places to do your dining.
Also Boston is really close and you can spend some time in the city as well.