This is what I would do within North America to maximize Tier points. This assumes you are flying to ORD, which you may or may not want.

4. ORD-EWR 60TP
5. EAR-LAX 180TP (beware of JFK-LAX flights as they offer Business Class)
6. LAX-DFW 60TP
7. DFW-ANC 180TP
8. ANC-DFW 180TP
9. DFW-HNL 180TP

This will give you a total of 840TP within North America alone. Maybe this can still be improved by having some obscure transcon flights which are not on the transcon list.

From HNL you continue onward to NRT where you do your CGK and HKG trips.

Didn't the OP want to depart "next month"? The direct DFW<>ANC flights don't commence until May 1st, IIRC.

This route starts in Europe, validates at 50862 miles and earns 1720 TPs on a DONE4:

GIB-LGW,LHR-HKG-DEL-NRT-SIN-PER-SYD-AKL-SYD-AKL-SCL-IPC-SCL-LIM-EZE-LHR-AMM-MAD-GIB

no North America, though :eek:

Edited to add: actually SYD-AKL-SYD-AKL would earn 360 TPs if you get on the BA codeshares (easily done at the airports IME), not 120, so the total goes up to 1960 :cool:

Edited further to add: obviously it doesn't satisfy the "must visit these places" requirement of the OP :o but I thought it was relevant to the topic title... plus it's a trip I'm going to try and actually book!

You are correct. I didn't think a DONE4 with (now) three weeks notice is realistic. The OP will be on tons of waitlists for that.

If the OP is flying before May 1st I would chose something like DFW/ORD to SJU as an alternative. More than 2000 miles but unfortunately only in business.

I would still go via HNL for the extra status credits. And it is a nice day to spend there.