There is a small Armenian minority in Greece (particularly the North) and their churches provide an interesting contrast to the numerous Greek Orthodox churches and cathedrals. This church is not open to the public, but you can enter the grounds and take pictures of the distinctly Caucasian style of the building.
The lighthouse is in the picturesque part of the waterfront and provides great opportunities for picture taking. Nevertheless, there isn't much to do at the lighthouse, and is really just a great way to enjoy the outdoors when in Alexandroupoli.
There are not many "sights" in Alexandroupolis, which is a city I suspect most people visit either to transfer to Turkey or to a ferry. Nevertheless, the Ecclesiastical Museum is wonderful and hold an impressive collection of Orthodox religious art (not just icons). The museum has a good explanation of the differences between Orthodox and Western iconography and how icons are made. It isn't air conditioned, however, so don't expect to escape the heat by visiting it.
If you are in Alexandroupolis don't forget to visit first of all the excellent blue flag beaches in and around the city. Then go to Makri, Maroneia, Evros Delta, Dadia Forest and do not miss the quiet but nature-rich Samothraki island
WWF supported forest and widely know all over the world for this "little" fella. Not so small though cause my dad told me that they are that big that they could lift off the ground a mature sheep!!!
The protected flora and fauna, of the forest is a joy to visit between April- June, when it is not that hot and warm enough to have a nice pic-nic.
When visiting Alexandroupolis you should definately spend a couple of days travelling all the way up to Evros. There are so many small villages where you will find all the tradition and the natural beauty of the region
If you visit Alexandroulis in July, try to get to the annual River Party(mostly Greek music, food etc.) of ARDAS some 120 kms north, at the border to both Bulgaria and Turkey.