In my last game on an earth type map, I invading germany from north of the Mediterranean. I had positioned a few of my missile cruisers and started bombing some panzers he had (he was building a space ship so I imagine it was just b/c he had no moneys to spend on upgrades). Lo and behold, when I bombarded these panzers, each bombardment only did one damage point. WTH? Considering that artillery could do 3 or even 4 damage, I'd expect that a missile cruiser could do at least 2, maybe 3 damage.
The navy is an extremely important part of your military. I think you have an unhealthy or even wrong view of the navy. A good navy can protect the city from invaders, it is almost essential in any invasions or landings in coastal cities or nearby cities.
A navy could mean the difference between a huge invasion and no invasion at all. If your foe is to invade your land he obviously need to send units across the sea, if you have the proper naval ships in place that invasion can end in catastrophy for your foe.
Having a good navy (especially destroyers) is vital in keeping enemy nuclear subs away. The destroyer is one of the most important, if not THE most important item in your navy, they have a good range of view, I recommend placing a few of these off your coast. Watch the fog how long they are able to see, make sure you place the destroyer so that it can "watch" all the way to the first tile of the coast, and the equal amount of length outside the coast on the other side. Spread destroyers so that each destroyer cover each other so that no tile is without watch.
If you can cover 8 tiles or more from the first tile of the coastline you are able to find nuclear subs before they enter your territory. The nuclear missile can be launched 8 tiles away so thats just perfect.
Speaking of naval bombardment having no effect, yes it does have great effect. Make sure you always construct your naval units in cities that give them free promotions. When you come to a specific amount of experience the naval units will get several promotions that will give them extra range, they will be able to fire extremely far inland, 4 or 5 tiles. There is also a promotion you can get one extra round of fire per unit-promotion. When you get to that promotion the ship will become extremely powerful, 100% more powerful.
For shore bombardment I recommend that you have a battleship in place too, it has bigger naval bombardment firepower. The ultimate naval offense/defense would be to combine with a carrier and stealth bombers.
Anyway, when you get the good promotions for your ships they will become tremendously useful and powerful.