Roughly 20 years ago, Victory Games released a series of Modern (at the time) Naval Games called the Fleet Series. They were a pretty good operational view of modern combat and had enough meat in them to recreate ship to ship battles (sort of). Each was set in a different part of the world. After a while, I managed to get all of them. Anyways, here is a guide to them.
A game turn is roughly 8 hours of time and it broken up into phases. In the morning you have allocate resources to strategic missions. This includes recon and interception. This allows you to strategically detect stuff, which means it stays detected until the next morning. You have to have something detected before you can attack it.
After that, a turn is broken down into three phases and you can only activate units of one type during each phase (sub, ship or air). This is where you conduct attacks. Attacks are pretty simple and have modifiers depending on circumstances and then there is a die roll. Combat can get pretty bloody. Scenarios range from the very simple to covering a whole theater. There are rules for combining maps, but each game is really meant to stand alone.
This was the first in the series and is set in the Mediterrean. There are units from the US and USSR (of course), Britain, Italy, France, and the various other countries bordering the Med. There are rules for whether countries will join the alliance (or leave the alliance). Combat uses a six sided die. This one was first and came at a time when there was a transition in the Navy. Cruise missiles weren't common yet, so they are treated as a special rule. The rules for countries leaving and joining the alliance is pretty nice as it seems to represent the fickleness of some NATO countries. There are also rules for limited Marine and Paratroop engagements, but it is very abstract.
This one was set in the North Atlantic and as such is probably my favorite. The rules are refined from Sixth Fleet and a 10 sided die is used instead of the six sider. There is a rule at the end for combining the maps, but the counters aren't quite compatible as the numbers are different to reflect the different dice. This one has rules for simulating a Soviet push across Norway (you start to lose bases as time progresses). This also has counters for Soviet SSBN's but they are very bad to attack (repesenting the fact that you don't want the war to go nuclear...I would imagine sinking an SSBN would provoke a nasty reaction from the Soviets).
This one is set in the Far East and ranges from the Northern Japanese Islands to just south of China and from Guam in the east to a little past Vietnam in the west. (the squashed the map around Guam to include it because it is a pretty important base, even more so now that the US doesn't have a presence in the Phillippines). This one added actual values for Cruise Missiles and tweaked some of the rules.
Set in the Persian Gulf and Indian Ocean. Not really that much different from the others except for the setting.
Set in the Caribbean and the Pacific around Hawaii to the Aleutians. This one added rules for the Stealth fighter.
One of the nice things about this series is that the rules are similar enough across the board that if you learn one game, you can pick up the others pretty quickly. The Scenarios are arranged in orders of difficulty and scope. The first couple only have one or two types of units. The rules don't get into the minutae that a game like Harpoon would but they are good enough to get a feel of modern naval combat. Each ship is represented along with an abstraction of their relative abilities (missiles and guns). The combat is brutal.
The far reaching scenarios are probably the best. They cover what amounts to war in a particular theater. Given the time that some of these combats would take, there's not too much in line of bringing ships from other areas, so you pretty much fight with what you've got. The rules cover things like armistices and victory points. Generally the side with the most victory points wins (or fewest depending on what counts). The rules are nicely written and easy to follow (although thick). At the end of each book is kind of a thumbnail of the Navies at the time these games came out.
Admittedly, these games are pretty dated in that there likely isn't going to be combat between the US and (now) Russia anytime soon but they make for a nice "what if". I'm not sure how realistically the capabilities are portrayed but from what I've read they are pretty close. You can add things like logistics and nuclear weapons to make things even more interesting. Weather is covered abstractly but can have an impact (especially in 2nd Fleet).
These games are long out of print, but they can had on eBay fairly reasonably.