I think you will find more to see in Nicosia than Larnaca if you only have one day. The Venetian walls are interesting and you can just wander around the old part of the city. You can cross into the Turkish-occupied part of the city by walking to the end of Ledra street (you will need your passport). It is quite easy. There are some interesting buildings to visit there, but mainly there are a lot of shops, many selling knock-off handbags (which will most likely be confiscated when you return to the ROC so I wouldn't advise buying them). There is an excellent archaeological museum in Nicosia. There is the Pierides museum in Larnaca, which I have never been to, because it always seems to be closed when I am there. In Larnaca you can tour the fort and wander around the Turkish part of the city where there is an old mosque and old buildings that are now artists workshops. And of course you can take a stroll along the Finikoudes Promenade (along the sea). You can also see the salt lake (dry in the summer, flamingos in the winter), the Sultan Tekke mosque along the salt lake, and an aqueduct, but you will need to have a car to drive to all these places. Public transportation in Cyprus is still in it's early stages.

You can take a city bus from Larnaca to Nicosia, but you cannot get the bus at the airport so it is a bit of a logistical challenge. I would recommend hiring a car. If you do hire a car, INSIST that you return the car with as much petrol as was in it when you got it. You may have to fight hard about this, but for some bizarre reason, they want you to pay for a whole tank of petrol and this is expensive if you only have the car for a day.

Going to Salamis is an option but you would have to hire a car and you would have to be sure that you can take it into the North (not all car rental companies allow this) and you will have to buy insurance prior to going to the North. Salamis is about a 30 minute drive from where I live and I live about 45 minutes from Larnaca. But if you do go to Salamis, you can also go to Famagusta and see the Venetian walls there, which are similar to those in Nicosia, except Famagusta is a port.

Jaymar01 mentioned going to Girne. The Greek name is Kyrenia not Lefkosia as he/she said. Lefkosia is the Greek name for Nicosia. But going to Kyrenia and Salamis in one day is pretty ambitious, especially if you only have technically half a day on the day you arrive and if you are departing the next day at noon, you need to be at the airport at 10:00am so most of that morning is not available.

My suggestion would be to hire a car and go to Nicosia for the afternoon. Then return to Larnaca for the evening and spend the night in a hotel in Larnaca. Have dinner in one of the many tavernas in the area and then have breakfast in one of the many cafes along the Finikoudes and maybe, if you are an early riser, you would have time to tour the fort in Larnaca. On the way back to the airport you can make a quick stop to see the aqueduct, it's right along side a main road.