I like Bruce's answer. Before considering taking any action, you need to understand that IF you were to do it - against recent SOLD comps, if the investment would have an ROI.
Sometimes a conversion is necessary to get the home sold. For instance, my parents were trying to sell a home of theirs a few years back. It was 2 BR/2Bath and a really nice ranch with all sorts of vaulted ceilings. Many potential buyers were like, "wow this is great but I really need a 3 BR". So after 30 days of hearing that again and again, dad took the dining room and walled it off from the foyer/lr area - and added a door from it into the "br hallway" area. Viola! A 3rd BR on the cheap. And then it sold very quickly thereafter.
With your home the way it is ... are there a good pool of buyers or do most of them want/need a 3rd BR. This needs to be understood.
You have 2 pools of buyers. 1 those who want a garage, 2 those who want 1 more bedroom than you have. Which pool do you wish to go swimming in? Is one of the pools bigger than the other or have more fish? That is what you need to figure out.
Could you add on a third bedroom some other way easily and reasonable so you would have both a garage and 3 bedrooms? And finally, what happens if you do the upgrades and do not sell quickly or easily?
If the conversion fits seamlessly into the decor and is run off an upgraded A/C, then it will be appealing. Changes or additions to the A/C are usually needed because you're cooling more volume. When you do that, your current A/C (which is likely old) should be replaced and upgraded to handle the additional living space volume. Consult a HVAC person.
If the conversion is 2 steps down into a dark room that the A/C doesn't seem to work right, you will have wasted your time and effort. If there is ample parking on the driveway apron or street parking is permitted, then you will fare better than having no reasonable place to park.
You should be aware that generally, even though the floor space is equivalent to a 3/2, people expect it to be priced cheaper because there is no garage. You won't be able to use the pricing for 3/2/2 except as a cap over your pricing. The more updating and upgrading you do, the better you will do in terms of pricing (maybe as high as the 3/2/2), but don't go overboard. Several articles have been published on the value of and whether you get your money back on updates/upgrades. Ask your Realtor for a copy.
You'll need a building permit for that.
Only if the construction project is permitted will it add value.
Technically you are remodelling, not a garage conversion. I would suggest "adding a bedroom" will sound better to a building inspector or plan check person, rather than 'garage conversion", which sounds like you are converting a parking space to a bedroom...which is not legal in most areas
I like the idea of adding the living space. However, I am not sure you will gain enough in the sale price. i'd run the numbers because construction is not cheap. But if it pencils out, go for it.