A tour from Cat Ba is not a day trip. You'd have to stay at least 1 night.
If you were to go there, the cruises go around Lan Ha bay. Same scenery as Ha Long but far fewer tourists and much cleaner water.
I did a full day cruise (9am-5:30pm) including kayaking and a good lunch on board for 340,000VND booked through my hotel in Cat Ba town.
Which hotel? Sounds like a great trip
Just book a hotel that suits your preferences. They all offer tours. On the excursion I was on, we were all staying at different hotels.