The Frost Science Museum and Perez Art Museum are right by Bayside downtown. It’s a nice campus and both museums are new-ish (maybe about 10 years old). You could easily spend 4-5 hours seeing both, especially if you are with kids for the Frost. Very cool sharks!

Which cruise line, OP? I’m considering something similar!

Miami Culinary Tours does an amazing food and cultural tour of Little Havana I highly recommend.

Another option is to rent a car and head to the Everglades and take an airboat tour. Make sure the tour company is approved by the National Park Service.

Bayfront is right near the port. There are touristy activities there like boat rides, Bubba Gump shrimp, a mall, bars etc... all for the cruise ships. You can also walk into Brickell and around downtown from there.

I’d walk around South Beach and also do a boat tour to see Miami from the water.

Walk around south beach (not the beach but Collins, etc) and watch the people emerge from the clubs. Very cool architecture.

Walk around Brickell

Frost Museum

You could explore Calle Ocho and get some Cuban food. Be careful with Cuban coffee, it's super strong.

We arrive early in the AM the day before a cruise. Our hotel will hold our luggage, but we’d like to do something before we’re able to check in. We have no real desire to head to the beach since we will be spending the week at various beaches. We will go if there’s absolutely nothing else to do. Our hotel is right near the port and on Biscayne Bay. Is there anything worthwhile to do in that area?