This is not a very solid list, more like my fresh impressions from the recent replays of the games.
Codename 47
The Massacre at Cheung Chau Fish Restaurant - very simple, basic, yet the absolute classic that introduced the social stealth in Hitman.
The Lee Hong Assassination - on the contrary, very overwhelming and complex level that becomes fun once you learn the map and start experimenting with opportunities.
Plutonium Runs Loose - brilliant atmosphere, an unforgiving level-design that tests you.
The Setup - mainly the atmosphere. A quiet asylum at a seemingly peaceful night turns out to hide a lot of disturbing secrets and becomes a warzone shortly after.
Meet Your Brother - maybe not that exciting in terms of the gameplay, but anything will go with Ort-Meyer’s monologue.
Silent Assassin
Invitation to the Party - the setting that is very Hitman’y, an interesting gimmick, and overall a nicer level than most of the H2SA missions.
Jacuzzi Job - very small, yet quite complicated level. Unusual setting.
St. Petersburg Stakeout — St. Petersburg Revisited - very iconic levels that have the most connection to the plot. Similar on the surface, but very different in the reality - the first mission is done by the book, and the second is a challenging improvising nightmare.
Contracts
Asylum Aftermath - very atmospheric mission, especially the first part. Though here I’m done with pleasantries to this level 
Imo, it’s quite bad gameplay-wise.
Beldingford Manor - very classy, hitmanish, and excellent in terms of gameplay location. I would have preferred it to concentrate more on the main building though, removing most of the open space outside and possibly even the rescuing objective.
Deadly Cargo - I don’t really see this mission as a replacement for PRL, but it’s a good one on its own. Very smart ideas with the SWAT wanting your target too (except, alive) and the target threatening to detonate the bomb.
Seafood Massacre - a worthy successor to the C47’s counterpart. Still love it despite a little bit tedious “Hide body in the sewers” objective.
Blood Money
A Vintage Year - great and classy level.
The Murder of Crows - there is something so immersive in the “city” levels like this one. Great atmosphere, great gameplay. (Random positioning of one of the targets and long route of another is not good for speedruns, I must admit)
House of Cards - yet another classic Hitman environment, that being a hotel. Waiting for the elevators and targets to arrive is tedious, sure, but I still love it.
A New Life - perfection in terms of gameplay. I consider it to be one of the most enjoyable levels in the franchise.