If the military base would have a cultural area (say, the smallest possible: 3x3 tiles) and no chance of flipping, then it ought to cost A LOT to maintain or otherwise have some drawbacks. Both the attributes, the culture zone and no flip, are reasonable: a military base does have an area of control (one reason why it is there) and culture flipping does not make much sense in a military context.
But, but... An immediately obvious exploit: Once you have a core civ with good production and a hefty income, you start cranking out workers and filling the world with military bases. (I assume a base would cost you a worker like the other improvements.) This way you get the land conquest benefit of the cities but without any of the disadvantages: unhappiness, corruption, maintenance of improvements, etc.
I _do_ think the idea of a distant military base (or "improved outpost") has merit. It ought to be possible to control a valuable strategic location, like the Panama and Suez canals, without building a distant colony. Which in civ would flip over to the enemy sooner or later, anyway.
Of course, you might say that the Suez DID culture flip to the Egyptians in the real world.
How about this:
Make several levels of "outposts":
1 - Outpost. Your basic "lookout" lifting the fog-of-war. Just like the current one in PTW.
2 - Army Camp. By using up another worker your outpost is improved into an army camp. Additional benefit: heals land units.
3 - Military Fortress. Yet another worker added gives this. Additional benefit: area of control (i.e. cultural border of size 1).
4a - Naval Base. One more worker and you get docks. Benefit: repairing naval units possible (but not constructing new units, of course!)
4b - Military Base: This time the worker added an airfield and the assortments. Benefit: air units (including missiles) can be rebased and repaired.
(4a and 4b are separate because not every military base has access to coast)
Costs should, of course, be editable in the editor to suit scenario needs but I think in the ordinary game they should be significant to prevent me from building hundreds of them. For example:
Outpost - 5 gpt
Army Camp - 20 gpt
Military Fortress - 100 gpt
Naval/Military Base - 200 gpt
For example, mind you. Would have to be adjusted by test playing, of course. The goal should be that you can build and maintain some bases, but not tens of them and certainly not hundreds.
And to spice up things

: Make a military base subject to a _conditional_ culture flip. Once a base would flip if it were a small size 1 city, the cultural conqueror has the option to either let the base remain there or demand a rent for it (e.g. trade window opens and you can then negotiate a rent for the next 20 turns). If no agreement can be reached then the flip takes place and the former owner can declare war without hurting his rep if he wants to. Naturally, if the other party is very weak he may not want to demand a rent in the first place...
(This would fit in with real world, too: Gibraltar is still British and Spain doesn't want to start a war for it. Hong Kong was given over to the Chinese when the negotiated lease for 99 years terminated and the Chinese were "frankly not inclined to continue it" and "would never accept such deal"

)