I'll agree with the others here - if you cant do something like a trans swap yourself, sell the car, the fuel savings vs the swap cost will probably not pay for itself soon enough to be worthwhile. Starting at 180k there's a question of how much longer will it last to begin with. Unless there is a strong emotional attachment to the car or a strong family pressure to not have you resell the car (ie its not really a gift they just wanted you to drive it) it makes more sense to start with something closer to what you want as the endpoint.
Ignoring that, swapping in an OD automatic would probably be easier than converting to a stick shift - no having to work up where to put the shifter and clutch and stuff, and if you pick factory models it might be as simple as pull the engine and trans out of the subframe with a cherry picker (not necessarily that simple mind you, different FWD's let you remove different parts of stuff easily), bolting up a new one, stick it back in, connect wires to factory ECU if its a supported transmission option, and realign the car doable in a looong weekend with two cases of beer. Please underline the "might be as simple as" with bright red marker though, when it's not that simple your offline for weeks trying to figure stuff out.
If you look for a geo metro or xfi the biggest problem is they are so light they rust to hell to the point of physical danger - the steering control arms rot out and one hard bump later you could find the left wheel aiming left, the right one aiming right, and no response from your steering wheel no matter what you do with it. Thats their main "you will DIE if you dont fix this" problem that I know of, all other ones are just the normal problems of a nearly two decade old car, including ones often abused or neglected because they were treated as cheap throwaways by the mentality of many of the buyers of them.
Rear wheel drive vehicles have the ability to change gear ratios alot more easily - either changing the rear axle, or adding an overdrive unit, or changing the transmission type. FWD are so compactly put together and everything so close there's rarely any way to change anything from factory configuration very much. Whatever engine, trans, and axle ratio you have is probably what you just have. That said it's possible that different axle ratios either exist for the car - it's even possible some gearmaker might be able to make a custom numerically lower ratio for you within the dimensions of the housing, probably for less cost than the mechanic quoted price for a transmission swap. These things are done for racers, I haven't heard of them being done for economy and there's probably a limit of how much you could change it though. However the changing of the axle ratio and fixing the speedometer error should be alot less work than a transmission wap and the total cost including machining the gears probably alot less, maybe even under $1000.
That all being said if you got friends to help do a transmission swap, you almost might as well stick in a VW diesel or something at the same time and go all the way.
