I used to take all city promotions, and have recently changed to taking almost all field promotions. Repeating a bit on what has been said already, but I'll add some details:
1. When taking field, siege weapons double as ranged units, largely eliminating the need for further ranged units.
2. I find myself attacking units more than cities. Killing the units is the priority. Once the AI's units are largely eliminated, it's then a straight forward and easy task to surround and take the city. But clearing the units out of the way is the hard part.
3. Logistics! My promotion path is almost always Field III > Range > Logistics. Why? Because of XP. Range will always be king, because it allows the unit to attack more frequently by bringing more enemies into range, increases the the survivability of the unit by keeping it out of range, and allows for greater concentration of fire per turn by allowing another ranged unit to fill the 2 tile away slot. But after range, always logistics. The strength is decreased 30% per attack, but XP is doubled! Playing as a warmonger, I am taking Elite Forces under autocracy (+50% combat XP), and also getting the oil strategic monopoly (+2 XP). All combined, every ranged attack is now 5 XP (2+1+2). So if a logistics unit can attack twice, it is now accruing 10 XP per turn. And an artillery can attack twice most turns without moving with having 4 range. The unit becomes pretty unstoppable. Pretty soon, it's easy to backfill the city promotions with all the XP. **I don't know if this is optimal play, but I do it because it's really fun getting the highly promoted units.
3.5. It's worth mentioning that Blitz on ships is even better with this XP strategy. Once I can produce a ship off the line with Blitz (Military Academy + Order + Bradenburg Gate) it becomes really easy to get a fleet with both the boarding party line AND hit points / city capture line. I just produce a Blitz melee ship by going BP III > Blitz. Attack a city twice per turn is 18 XP (5+2+2)! There is really no risk of loss as the ship can move out of range after attacking due to the blitz promotion. If you can get a blitz ship with the full hit point promotion line and dauntless, it will never sink. Fun times!
I have never found splash very useful. 5 hit points (on immediately adjacent units only i believe) doesn't seem to make an impact to me. It is generally considered to be a good promo? That would surprise me.