There is only one reference to Rhodes in the New Testament scriptures. Rhodes is a port of call on Paul's so-called third missionary journey: returning from Achaia to Jerusalem with financial support for the church there. There is no indication whether Paul stayed in Rhodes for any length of time, or simply moved on straight away.
Because Rhodes is the name of both the island and principal city of the island, there is a tradition that identifies Lindos as the location of Paul's visit. Dr Mark Wilson dismisses that possibility here, as the northern harbour(s) of Rhodes provide a more direct route between Cos and Patara. Nevertheless, if you're on the island, Lindos is well worth a visit.
1 Maccabees 15:23 notes that Rhodes was one of a number of cities which received a letter indicating the support of the Roman republic for Jewish leaders in their struggle for control over Palestine in the inter-testamental period.
I was able to visit Rhodes in October 2014: a trip which included Cos and a number of locations in western Turkey. An account of that journey is available here.
I based myself in Rhodes, just outside the walls of the medieval city, arriving late on a Wednesday evening. The next day was a double acropolis day: a hired scooter to visit the spectacular acropolis of Lindos; and, later in the day, a walk to the acropolis of Rhodes.
The next day I took a very enjoyable stroll through the medieval city with its spectacular walls and gates, and then visited the harbour (where once stood the Colossus of Rhodes) and the Archaeological Museum of Rhodes. The museum is housed in the former Crusader period hospital of the Knights of St John. It contains a wide range of artifacts from various periods in the history of the island. That evening I continued my journey, by ferry, to Cos.
Click here for a Google Earth view of Rhodes.
The main features of the acropolis are the standing columns of a Temple of Apollo, the restored cavea of an Odeon, and the well preserved stadium.
The entrance to the museum is visible in Google Earth Street View here.
Of the many gates in the walls of the medieval city, one is dedicated to St Paul. Memorials to Paul's visits are all part of the Paul follower's interest!
There is no evidence that Paul visited Lindos but if you're in Rhodes and have the time it is not to be missed.
The small chapel at St Paul's Bay south of the acropolis belongs to a wedding company - access is very uncertain!