Awful: Prince (duh!), Tactician (>$4), duration cards, Island, a knight (unless you got it from the Black Market deck instead of a knights pile), Feast/Deathcart/other self-trashing cards other than Hermit
Bad because really dangerous: Remake, Rats
Pretty bad because dangerous: Bishop & other forced trashing cards
Might be bad due to forced play of actions: Throne Room
Suboptimal: Shanty Town, Menagerie, Treasury(>$4)/Walled Village, Fortress, Watchtower/Library/JoaT (unless there's a discard attack)
Good: everything else -- Monument, Smithy, Militia, Scheme, etc.
Awesome: Prizes
If you draw Prince with only one possible "suboptimal" target, odds are you want to Prince that card. A minor bonus blows up. Prince of Pearl Divers, that's an extra card and action every turn - it's like starting every turn by playing a Lab and a Village (and hey you get to do the Pearl Diver thing). So I mean. Prince of Fortresses? Go for it. Prince of Watchtowers, that's not what you wanted, but drawing an extra card every turn is a lot better than waiting to draw Prince again and see if you are luckier next time. Okay Prince of Jacks is not good except under attacks, but Prince of Menageries, that's pretty sweet. Prince of Treasuries has no issues when it's possible, you don't get to put it on your deck and hey do not wish to either.
For that matter, one-shots are bad since they don't work, but if you draw Prince with Death Cart and no other targets, man, Prince the Death Cart and hope you keep drawing actions to feed it. When it's not worth it, let it go. You only need it for a few turns to make out.
Forced trashing is sometimes bad, but not Bishop, that's a deck, the Prince of Bishops is making you VP every turn.
Prince of Thrones will usually be great, but obv. you might have a deck where it was too scary. It's not a question of if you'll draw that Remake; it's when, and what with. Well, the game could end before you draw it.
The problem with Prince of Ruined Libraries is that your deck probably has more Ruins and so that extra card is not so hot. I might pass there. Prince of Abandoned Mines I would at least consider, how big is my deck anyway, maybe big enough that I should just live with this.
Sea Hag is a poor target if the Curses are low, and since you have a Sea Hag, they probably are.
By suboptimal I meant that when Prince'd you're not getting the full value of the card, so maybe a $4 card is acting like a $3. (Reaction/Bane cards would be in this category too.) What you said indicates to me that if your Prince is matched up with a $3 card, it's likely you'd want to Prince it immediately than wait around for a $4 card. That makes complete sense to me. Even if it were guaranteed you'd match up your Prince with a better card next time, that's N hands until your Prince comes around again, so that's N hands you won't get be getting the benefit. Normal opportunity costs in Dominion are not this high! (Normally you pass on an opportunity 1 time while it cycles, not N.)
All the rest makes sense also, except that I need to test Bishop OTB to convince myself of that. From when you and I tried out the forced trashing at the start of every turn, I know that this aspect can be a blessing and a curse (but always fun). There is the victory token aspect, but my worry is being forced into a situation where I'm gaining VP every turn trashing small treasures, while my opponent is buying Colonies. Maybe the thing that saves me from this is that by the time I have a Prince, I should also have a large enough deck... Anyway, I've arranged to start trying it out OTB with somebody today, and I'm looking forward to that!