Here's a quick breakdown:
Naval Aviation - not enthusiastically pursued. Navy doctrine forsaw an area of operations within the Med. Sea, so they argued that they would be within land based range. This turned out to be a serious hindrance to the Regia Marina, as their land based air support was not reliable or consistent. However, Aquila was almost complete at the time of the Italian surrender.
BB - the Italians performed exceptional refits on their older WWI dreadnoughts, the two Cavours and the two Dorias. These had their 12" guns rebored to 12.6" and removed midship turrets for expanded machinery space, and picked up some DP guns. They were fast, 27-28 knots, and would have been well suited to carrier escort duty, if they had a carrier to escort. They still had weak armor, and some argue they were better labeled as battlecruisers. These were reinforced by 3 new units, the Littorios, which were roughly on par with other nations new "treaty battleship," although slightly heavier at around 40,700 tons.
Cruisers: The Regia Marina had the old German Strassburg, renamed Taranto, and the old cruiser Bari. Newer units included the two Trento treaty heavy cruisers, followed by the four Zara class CA, and finally the Bolzano. As far as CL are concerned, she had the fast but flimsy di Giussanos (4 ships), two Cadornas classes, two montecuccoli class, 2 D'aosta class, and two Abruzzi class CL. THese were collectively referred to as the 1st-5th Condottieri classes. These were reinforced by the Capitani Comani class CL, three ships, completed in 42-43.
Destoryers - too many to go into detail, but they were generally plagued by short range due to forseen Medit. ops. They also did not pack DP guns, and were vulnerable to aircraft. Italian naval ships in general suffered from lack of adequate AA guns.
This is getting long - but you can look up the submarines. Italy had produced some fine sub designs, and some failures as well...
All said - Italy saw her rival as the French in the Mediterranean. As France fell, a bold Regia Marina that actually committed itself to combat could have changed the strategic situation in the Med., especially with the RN having to cover the entire globe. However, the Italians never seemed to want to risk their ships in a major engagement with the RN, which defeated their whole purpose for existence. Interesting fact - the USS New Jersey covered 220,000 miles from 43 to the war's end, and Italy's 7 BB only steamed 80,000 throughout the entire war.