Personally, I almost never use the admiral's instant healing ability. It is only a matter of taste, but I don't like to lose the admiral-bonus without a lasting effect. Therefore, I would really prefer a tile improvement as second ability.
Regarding the "surreal" aspect of water tile improvements:
I think, it is just a matter of imagination. The civ-map doesn't necessarily show every small detail. Why not assuming, that a coastal fortification is built on a small island (to small to sustain a city, but more than large enough to sustain a military outpost) or on a small peninsula reaching into the coastal water tile?
Therefore, I want to promote my "Costal Fortification"-idea:
- buildable at coastal tiles (adjacent to land only) anywhere on the map, but not inside other culture influence zones
- converts a 2 hex range of water tiles into your culture. (Though no culture flipping of already acclaimed enemy borders.)
- casts a ZoC of 2 hex against enemy ships. (= slows ships down like the Great Wall does on land.)
- can attack ships within 2 hex range.
(- ships may heal additional 10 HP/turn if stationed inside. This is not really necessary, as the cultural influence zone itself already allows ships to heal.)
The idea behind this:
a) helps to defend coastal cities against raids
b) helps to defend naval trade routes against raids
c) may control straits (I love especially this aspect)
d) may be used as sea outpost far away from the own empire.
--
furthermore:
e) is very close to the Great General's ability but not exactly the same.
f) is longer lasting and not so out-of-time in early eras than mine fields.
The "flagship"- and "city building"-proposals are reasonable but quite "unseeable" and very Civ4-ish. I would prefer the tile improvement all the time.