I'm actually entered in NYC half for next March, and also have run Chicago, and Shamrock half and full I've also spent a lot of time on that Potomac River Run course.
a) if money is no option (which is highly unlikely), and a spring marathon is off the table, then I'd do either NYC or Shamrock Half in the spring. In the fall I'd register for three races: Chicago, Mohawk-Hudson in Albany, NY, and CIM. Chicago and Mohawk-Hudson are on the same day in October; CIM is in early December.
Plan on your sub-3 attempt at Chicago. Watch the weather as race-day approaches; if it looks too warm, then reroute to Mohawk-Hudson.
CIM is your second back-up, if you either get injured during the Chicago training cycle, or if Chicago doesn't go the way you want. There should be 8-9 weeks between the two next year -theoretically enough to recover from Chicago and do a small bit of training before CIM.
(I'm trying the Chicago-CIM double myself this year - I'll try to remember to check in and let you know how it went).
b) as for individual races:
-NYC half. I've yet to run it, but everyone I know who did it last year ran PRs. You can make up a lot of time on that west side stretch. And purportedly much easier logistics than the NYC full. If you want revenge on NY, I recommend this.
-Shamrock half. Great race - my half PR is from there. You'll usually get pretty good weather, though it can sometimes be cool or warm. It will almost certainly be windy, but the wind will be from the northwest, meaning it will be a headwind for the first half (when you have shelter via other runners and some trees), before you ride the tailwind home. People regularly PR there in windy years.
-Shamrock full. Also a great race. It can be very windy, but even in those years many people PR. It's very well managed, and will be nothing like your NYC experience. Especially if you stay at a hotel near the start/finish. It is important to note that a) the course is boring and b) you may be alone at times if you're going for sub-3. I ran 3:08 there, and I was alone for periods of time in the second half. However, you get to chase down the walking half-marathoners in the last 6 miles of the marathon, which actually helps a lot (there's not enough of them to really be an obstacle).
For either of the Shamrocks, the hotel prices on the boardwalk are jacked up for race weekend. Some to NYC-esque prices.
-Chicago. If you have to put all your eggs in one basket, choose this one. It will be the opposite of your NYC marathon experience. Stay in the loop and walk to the start. The race is very well managed and the course is extremely fast, with plenty of people to drag you along at 6:50 pace. The course is also mentally easy - there's enough turns to keep your mind interested, and nearly the entire course is packed with crowds cheering. The only issue here is that it can be warm (which is why you pick back-ups).
-Potomac River. I would NOT choose this race for a sub-3 attempt. It is inexpensive and logistically easy, but trust me, twice out and back on that course has to be mentally exhausting. Especially if you're running by yourself, as you almost certainly will. Plus the crushed stone surface is a bit slower than pavement, IMHO. Not by much, but a few seconds a mile. Which might be the difference between 2:59 and 3:00. Potomac River is a great option for people wanting to cross another state off a list, or to knock off a BQ. Or to run a marathon for the heck of it while staying local. It's not a good marathon for a sub-3 attempt when you're on the cusp.
Other races you should consider: Mohawk-Hudson in upstate NY, CIM in California in December, Grandma's in Minnesota in June. All will involve a fair bit of travel for you. But they are all very good courses. And unlike Chicago and Shamrock, they have rolling hills. Since you train in a hilly area, you may find that a rolling downhill course like CIM suits you much better than a pancake flat course - you're used to hills, but may not be used to 26 miles of using the exact same muscles.
c) final thought - I suggest going on the USATF website and pulling up a list of Olympic Trials Qualifiers and where they qualified. Especially on the women's side. That may give you an idea of the best races to target. I guarantee that you will see CIM, Grandma's, and Chicago on that list. And I would expect to also see Mohawk-Hudson and Shamrock there.