You really need to get some guidebooks and start doing some heavy duty research, We can tell you what WE want to see - but not sure what tell interest you.

I will say that Genoa is not a typical stop on a first visit - and I wouldn;t stay anyplace just because you can get a free hotel there.

Also, while Naples has some sights, and easy access to Pompeii - it;s early for a trip to Capri (ferries may still be on winter schedule and water very rough).

Once you have decided what your interests are - roman ruins, churches, history, fine dining, architecture, wine tasting - clog dancing, hang gliding, etc - people can make specific recos. I hope you know that this isn't beach weather in Italy.

How long do you plan to stay in Italy? The duration of your trip is important if we are to make suggestions. I agree that Genoa is not a typical stop although we have enjoyed short stays there twice.

In March, you might be best advised to split your time between Venice and Rome, depending on how long you plan to stay. There is plenty to do in both cities and you can take day trips from each.

What the previous posters pointed out may be the difference between budget conscious and value conscious. I am not sure what you meant by budget conscious.

For me, budget conscious means minimizing the cost -- without considering the impact on the overall "value" one takes away from the even. An example I have seen among my acquaintance is taking time to go to Berner Oberland, but stay in Interlaken without going into the mountains because it was not cheap. So they saved money, but what did they get out of the visit?

Value conscious means optimizing value within the cost constraints. This requires more thinking and trade-offs. This one asks: within the cost constraints, where can one go to optimize the "value" one gets out of the event.

I have also been to Genoa, but I had a specific objective that could only be accomplished in Genoa, and I also happen to travel through the city. Without a clear objective, I would not have gone there.

>>>Our Hotel points allow us to stay in the cities above.<<<

Which hotel chain? Many times, chain hotels are not well located in Italian towns.

Also, even though I have tons of Marriott points I am not using them on our next trip to Italy. Sometimes they are not well located unless you have a car. Although we plan to go to Genoa soon I definitely would not consider it for a first trip. Perhaps you will enjoy a day trip to Verona if you like Romeo and Juliet? You cannot go wrong with just Rome and Venice. Maybe add Naples for a couple nights, but remember Capri would not be a budget day!

We did stay at the Renaissance Naples Mediterraneo Hotel (marriott) and it was just fine. There is a great hop on/off bus tour in Naples, go to Pompeii with public transportation (watch for pickpockets!) look at the castle in Naples. We also went to Capri, but it was in the summer...
Remember Rome is nearly inexhaustable, and on a romantic honeymoon, you can just lose yourself in Venice. We have been there a number of times and do not tire of it.