Apologies for long post.

This is NOT, it should not and do not want it to be a combat focused game, however being a military power could add some interesting game play, diplomacy and economics.
Certainly agree with the need for a more robust Navy and possibly the addition of a Military Navy Port, together with a Military Air Force base with fixed wing and rotary aircraft.
I also have seen suggestions for military parades, and Armed forces residing at their bases.

Such uses could be when 'enemy ships near Island' appears, we could actually see them and engage, with Air force and Navy, Air force and Navy could engage enemy ships, and Navy and Air force could bombard targeted locations on land (using Naval craft as artillery to save adding too many new features) as just having external enemy units appear on an Island is annoying - seeing them have to use landing craft would be a nice addition.

The inclusion of the bunker was welcome, perhaps Ground to air defence could be integrated?
Well measured handy caps would have to be introduced for both sides, the scale and types of enemy Naval and aircraft could be proportional to era how much you have provoked them, their power/economy and alliances. Particularly strong Tropican allies could have a mutual protection option whereby they would assist, potentially permitting those who do not wish to be militaristic focus on diplomacy and rely on Allies for military force (perhaps requiring a constant trade route and permitting them to have a base in your territory).

Building a Nuclear arsenal could end such attacks from other states and you could choose to target a particular nation to pacify or anger them entering a 'cold war' type standoff with proxy conflicts whereby you are no longer under threat from Nations, just the usual rebels(funded by the targeted nation). If an enemy attacks or have poor enough relations going to you could choose to 'fuel missile' and they may stop and go away, if they don't you could actually launch, triggering a countdown until it hits which may again pacify said attacker with the ability to cancel the launch "self destruct" or similar prior to timer running out. If you let the missile strike it could remove or reduce their the nation from the game politically, economically or both, permanently or for a good period of time. Such action could sour relations for a long time or permanently. Might relations slowly repair over time with actions like "foreign aid" in money or goods demanded? Would such action damage all political relations, just that Nation or their allies as well?
Might it take a time to build a new missile in the existing silo, could more than one silo be built, or nuclear armed submarine for variety being the only two available?
A few things to work out but would enrich this aspect of the game - all we have is a single somewhat underwhelming aircraft carrier.

Some of these actions could be linked to an Alert Status such as DEFCON 1 through to 4 (fuel missiles, El Prez to safe location, Garrisons called in etc) and 5 active conflict. Actions for the various statuses could be player adjustable.

I also have seen suggestions for military parades, and Armed forces residing at their bases.
Further El Prez having appropriate protection such as appropriate road and maritime transport as well as a body guard that could be Player adjusted for the times. With included "Emergency protocol" for El Prez where he would be whisked away to his palace or VIP Bunker under escort. Triggered manually or automatically at specified Alert status.
'Public fear' measure; e.g. More security for El Prez or in VIP Bunker, higher DEFCON - increasing fear- inverse true. Fear impacted by significant political situations. Fear lowered with military parades, Civil Defence measures (emergency radio options in Tropican comedic fashion - option to attempt to alleviate fear through denial or expressly stating emergency instructions), sirens and similar - functions required rather than new structures), Civil defence exercises, military exercises.
Some Public Fear dependent on political alignment, some universal.
Admittedly much required for balancing and game mechanics.

Buildings suggested;
Military Air Port; Military Naval Port; Anti air defence (possibly visible upgrade to bunker); VIP Bunker (could be an upgrade to Palace, though preferably different location); Civil Defence (also acts as fire house in peace times?); Public Civil Defence Bunkers (And possible edict subsidy for residents to construct in house shelters); 'No Fly Zones'; pre positioned defence structures activated at certain Alert Statuses (alert status affecting tourism); 'Militarised Police' Upgrade visible to police and station either constant, player toggle or upon specified alert status providing defence for Civil defence bunkers or combating organised crime.

Units suggested; usable aircraft (fixed wing fighter bombers and rotary ground and ship attack, ability to instruct military units to engage specific targets and patrol, Player adjusted DEFCON or defence status with pre determined actions), Ability to target specific Nations with Nuclear weapons to simulate MAD doctrine (mutually assured destruction); Militarised Police.

This is a lot, and runs the risk of making a great game overly militaristic - it would have to be rare and mostly result of player actions so is avoidable for those who would not enjoy the military aspect. Does open plenty of edicts, constitution options, more weight to political relations and provision of tasks.