I'm playing the original Age of Wonders. Is migrating a new race always the best solution when dealing with a conquered city populated by a hostile race? According to the manual you can get them to like you if you do a lot of things they like (upgrading the city comes to mind, what else is there to do?), but looks like an unnecessarily complicated process when you can just replace the whole population in 3-5 turns. Not to mention that unless you keep a large garrison at all times, they will rebel faster than you can say "ethnic cleansing". I'm playing the "good" campaign so it seems a weird thing to do for a faction that believes in peaceful coexistence...

Also, any opinions on razing cities? Is more cities always better, or can scorched earth come in handy?

Yes. Hostile races are difficult (practically impossible) to maintain. They'll just desert you.

Against computer opponents I don't raze that much. Only sometime when the city is deep into enemy territory. Against humans I tend to raze more often.

I generally role play this aspect of the game.
If I'm Good, I raze/loot the smaller Undead cities, migrate the rest of Evil cities, and improved living standards for the Neutrals. Often stone walls are enough to keep an otherwise hostile city content, but units produced will rebel.
If I'm Evil, I'm more likely to raze or loot, depending on size of city, and how useful it may be.
Most campaign maps are so short that there's not much point in building up cities anyway.

Unless you have something urgent to do with the garrison, migrate. With a bit of luck you can migrate without a garrison, as city morale is a bit overtuned, and "unrest" only means 10% rebellion chance per turn.

I do like the raze if I have Animate Ruins though.

There are limited things you can do to improve race relations. Building walls, migrating to that race, upgrading, and maybe casting rejuvenate on their cities. Relations also gradually return to normal over time. So not really worth the effort to try to improve relations with races of the opposite alignments. Mainly just worth doing for races that are neutral towards you and you want to buy some of their other independent cities.

On a long map it may be worth the investments if you're Good and cast the Tranquility spell.

Incidentally the recent hex editing mods all address city morale being too forgiving (I refer to the AoW+, AoWx, Ziggurat, and Evolved mods)