The first place I would look is on the EMODnet website (their central portal provides access to a variety of marine data). As an EU Network it will not have information on countries outside of the EU (except those with a agreement between themselves and the EU like Turkey) bordering the Mediterranean Sea. But it will be a good start...

For ports, offshore installations and activities try this link to view their data (to download follow the links for search under the Search Data tab):

http://www.emodnet-humanactivities.eu/view-data.php

With regards to locations of Mediterranean Sea ports I would also start by having a look at the World Port Index published by National Geospatial Intelligence Agency in the USA (you'll be able to fill in the North African and Levant coasts with ports) see below link for GIS data download:

https://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0015

For additional port data and statistics you might have to search for data from the ports themselves or perhaps see if you can contact European Maritime Safety Agency (EMSA) who might hold this data.

I have processed all the above mentioned datasets, into ESRI format, already so if you need a hand in organising it I could help you out, feel free to drop me a message.

Cheers,

Simon

I can just give you the names of the three most important ones in the region I live in: Rijeka, Croatia; Koper, Slovemia and Trieste, Italy. I guess they have their web sites with additional information.

From Valencian Community (Spain) you can find the list of every Ports (commercial and non-commercial) with coordinates and services provided.

http://www.habitatge.gva.es/es/web/puertos/puertos-cv/puertos-gv-p