Honeymoon for under $3k in March without immigration

My husband and I are both international students on student visa. We are looking for some place tropical (probably central america but open to anyplace outside US) in March 2025 from US which wont require a immigration clearance when entering back into US.

What are some good recommendations for under $3k? We just want a relaxing vacation with beaches and pretty cities to walk/drive around (may be snorkeling or few water activities). (We both are strictly vegetarians so food might be a problem but willing to survive on bread for a pretty place!)