It's also important to consider not just Return on Investment, but Opportunity Cost. that is, what could you have done instead.
Let's look at some of the other ways you can get health:
* Trading
If you have 2 Corn, and 0 Wheat, trading that to an AI gets you a +2 in cities with granaries in ALL your cities with 0 hammers spent. Always be on the lookout for trades. On higher difficulty levels, you'll often be looking to trade resources for Gold, but on lower levels the AI rarely has much gold to trade, so swapping for resources you lack is just fine.
* Expand
Usually when you get more land, you get more health resources. On many maps the health type resources are clustered, so you have to get farther away from your capital to diversity, and of course, diversification is the key, since any number of the same thing still just gets you +1 health. Settling a new site that opens up a new health resource is better than building an aqueduct.
* Buildings
@Fippy did a great write up on Granaries, Harbors, and Aqueducts. Let me add in a similar analysis of Grocers, Supermarkets, and Hospitals to round out the health buildings. Note that Fippy didn't even mention those buildings... we'll see why.
* Grocer
Costs 150 hammers.
Benefits - a potential of +4 health but it's not guaranteed, +25% G, lets you run 2 merchants.
- The +25% G might seem like a good passive effect, but generally your goal is to run the slider as close to 100% science as possible, so, the +25% G is really much less in practice. You're better off running Merchants, building wealth, Fail Gold, or getting money from conquest. Investing in gold buildings is very situational, and usually limited to banks in shrine cities, for example.
- The option to run Merchants is nice. If you're running Caste System you can do this already. Merchants get you a +3G, plus they contribute to Great Merchants, which can be worth +1000 G.
- The passive effects on this building are effectively none. You have to choose to run the merchants, and if you're running Caste System, you get that benefit anyway. The +25% is minimal if you're managing your spending via building wealth or running merchants, or FailGold.
* Supermarket
150h, +1 from Cow, Deer, Pig, Sheep - potentially a +4. Passively +1 Food.
It's not bad really, but its available so late it just doesn't factor in that heavily. Still - chances are you'll have a lot more access to Cow Deer Pig and Sheep than Bananas, Spices, Wine, and Sugar. And the +1 Food is a passive guaranteed effect, so it really can net you +5 Food in a big city in the late game after factories are built and labs if going to space. I'd build it before I built a grocer or an aqueduct if it was late and I was having health problems. ...late game, you're probably better off just investing in spreading around the Sushi corporation for the raw + Food rather than worrying about health.
* Hospitals
200h
+3 Health
Heals units extra per turn.
..the passive effects are poor, and the building comes in late game, and it's even less efficient than an aqueduct. (66h per health versus 50h).
So, in this order for health you'd generally want to build:
Granary, Harbor, Grocer, Supermarket, Aqueduct, Hospital.
Most cities, I stop at Granary, or Harbor.
...in the order you want to acquire health I think it's more like:
* Expand to capture resources.
* Build Granaries.
* Conquer opponents to take their stuff.
* Trade with opponents to fill out your gaps.
* Build Harbors.
* Build other stuff.
...the main thing I've learning going up from a 50/50 Noble player to a 50/50 Immortal player in the last 2 years is that return on investment and opportunity costs of buildings is quite high. Those 100h you could put into an aqueduct could be another city in the form of a settler or 2 catapults, could mean better tiles worked from extra workers, or just gold or beakers, all of which have more benefits.