I like flying between between bigger airports, or airports I know have ILS landings on every runway, (when I'm learning an aircraft, or practicing a technique) but beyond that, I've usually used my home airport and JFK, or MIA to JFK if I want a longer flight, I'm looking for better ideas for practice, I like those routes because there are no mountains to interfere and there's decent scenery along the way.  Maybe someplace out west? Maybe Europe?

There are a lot of great routes all over the world, what type of airplane do you like flying? When I have a few hours or more to enjoy I jump around the world, I look at airport schedules in flightaware or fr24, flying in America and Australia is best for Flightaware as they usually post the filed flight plan which is fun. then as a bonus I load liveatc.net and get liveatc for the airport and area if available by looking at the world map on the main page. In Europe I like taking off from EHAM it is well covered by liveatc and flying the PMDG 737 for Transavia or KLM to many destinations like Spain and Sweden.

Are you looking for specific routes or for specific destination airports with challenging approaches?

 

The typical challenging approaches for big jets are:

LOWI - runway 08

LPMA - runway 05

LFMN - runway 04

KJFK - Canarsie 13

VHHX - Kai Tak IGS 13

 

But there are a lot more...

 

You could start flying KJFK-LFMN and doing a VOR 04 approach, for example.

London city airport

 

EGLC

Now I re-read the OP, I think he's looking for shorter routes. So my favorite short routes are flying the PMDG 777 freighter. Cargo routes that are short, off the top of my head, (not used FedEx until FSDT comes out with MEM...) Aerologic fly EDDP-EGNX-EDDP great aerosoft and uk2000 scenery for both airports. Also EDDF-EGNX-EDDP and EDDP-EBBR-EDDP. Lufthansa Cargo fly KORD-KIAH and CYYZ-KIAH. Emirates Cargo, Qatar Cargo and Air France Cargo fly MMMX-KIAH (mostly empty so they sometimes go up to FL430). Emirates and Qatari fly MMMX-KLAX also mostly empty. Air France Cargo fly EIDW-LFPG. Lufthansa Cargo fly KATL-KJFK. EGCC-EDDF and ENZV-EDDF. Around the world, Aerologic fly VTBS-WSSS and WSSS-VOBL. All these airports have great addon scenery options and most flights are less than 2 hours.