Overview
Despite everyone saying you need at least 2-3 days to do it justice, we only managed a day trip due to time constraints and visa reasons. Let me say upfront: Rhodes is clearly a level above the other Greek islands. The Old Town is superbly enjoyable. I completely agree with those who recommend more time, but if the choice is between never seeing it and a day trip, I'd pick the day trip every time.
What to See
The Rhodes Castle is a must-see, and the Street of the Knights should absolutely not be skipped. You can also walk the full perimeter of the castle walls from outside for beautiful views. Make sure to get lost wandering the Old Town streets.
The acropolis area has nothing worth the trip, but the viewpoints just behind it are absolutely stunning.
The new town part is pretty ugly. No need to explore it.
Food & Drink
Seafood and fish are superb. We had swordfish at a restaurant called Taverna Costas and it was really enjoyable.
Tips & Advice
The number of planes landing on the island is genuinely staggering. One lands every five minutes. I doubt Izmir gets this much air traffic. It really shows the level of tourism these guys have achieved. Quite sad from our perspective. If only we could properly leverage the opportunities we have.