Where to go in January for food, swimming, and mountains

Hello, my partner and I are getting married this month, but are planning on honeymooning in January. She wants to spend a day or two in a more populated city with a nice hotel/resort ideally near a beach.

That sounds good to me, but I'd also like to do some serious hiking in either the jungle or mountains. She's a hiker too and would be willing to camp for a night or two as well. We've both done some big mountains, so snowy peaks are ideal, but we would settle for some tamer hiking as long as we can go unguided.

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At this point any advice would be appreciated, so let me know!