Before we had a baby, we used to stay in hostels and rooms with shared bathrooms. After Baby V arrived, the first thing I need in the room is a private bathroom.
A cruise is a great if you like the idea of having the same room for 6 to 7 days, while seeing different destinations. Our first vacation with Baby V was on a cruise, and we quite enjoyed it. We did not have to cook (the cruise had fresh Indian food every day!), we did not have to check in and out of hotels, lugging our baggage around, and the cruise itself had enough entertainment if we wanted stay on it for a day. We got a balcony room (slightly more expensive), but I enjoyed sitting out on it with the baby, or relaxing with my husband when it was nap time and we needed to have a conversation.
If you feel taking the baby in a huge ship is too adventurous, an all-inclusive resort is a similar idea. Although I’ve never stayed in one, it would offer all the luxuries of staying put in a place with food and cleaning taken care of (though, you’ll have to find enough things to do in the one place). For a first trip with baby, a resort is probably a good idea so you can test the waters.
If you’re going to a new country (or state), I prefer booking an apartment to a hotel room. Apartments (or houses) usually have a lot more space, and extra rooms so you can spread out (and even give the baby their own room). Bathrooms are more spacious. And I like having a kitchen (instead of just a kitchenette). I’ve used AirBnB extensively to find great places to stay, and also booking.com, where you can filter for suites with kitchens. I usually try to base ourselves in a city, and do day trips from there, so that our schedule is flexible.
When you travel with a baby or toddler, know that your plans are always going to be flexible, and you might be spending more time in your hotel/apartment than planned. So, make sure it is a nice space, so you don’t feel like you’re closed up in a small room.