So, if I fly LAX-NRT, getting in at 4:40 PM, my choices seem to be:

1. NRT-FUK JL3057 7:50 9:55 (train to Hiroshima doesn't seem to run that late)
2. NRT-KIX N327 7:00 8:50 (flying NW instead of JL)
3. NRT-ITM JL3007 6:30 7:55 (not sure if this is a legal connection)
4. Overnight in Tokyo, fly HND-HIJ, HND-FUK, HND-???

Anything else?

What do people recommend?

Which airport is easier to get to Hiroshima from?

If you want to avoid overnighting somewhere on the way, then I think 3 is the best of those options. 1hr 50mins should easily be a legal connection within Terminal 2 (I assume you will arrive with AA at T2?).
On arrival at ITM, you can take a cab or bus (25 mins) to Shin Osaka Station. And from there it's a 90 minute Nozomi train ride to Hiroshima.
Last departure from Shin Osaka to Hiroshima is 10.29pm, so you have some room in that plan for delays.

Just for your reference --- A 7.57pm Nozomi Shinkansen departure from Shinagawa (which you could easily connect to) would get you to Hiroshima at 11.56pm. That would be a rather less complex journey (one train change). It would get you to Hiroshima slightly later than the flight + train plan (assuming the flights are all on time). And it would be slightly more expensive (but the difference might be insignificant if you take a cab from ITM to Shin Osaka).

Yes, I'm arriving on AA in T2.

The Japan Rail Search has an entry for "Osaka Airport" -- is this the same as ITM?

Your alternative suggestion, using Shinagawa, if I understand it, would be to land in NRT, get to Shinagawa, and then take the Shinkansen to Hiroshima? The Japan Rail search site makes that look exceedingly difficult, suggesting I'm better off flying to Osaka, as otherwise I'd have to change 4-7 times to get from Narita to Shinagawa. Since the AA flight is scheduled to land at 4:40 PM, I used a 6 PM departure time from Narita in the search. Probably I'm not searching correctly.

Well... 5.48pm Narita Express departure from Terminal 2 would get you to Shinagawa at 6.56. But if you're concerned that you would not make it onto that train ....

Instead, you could get the Narita Express (6.19pm departure) to Tokyo Station (7.19pm arrival).
Then the Nozomi Shinkansen at 7.50pm from Tokyo station.

However, I like the look of that ITM route. (Yes, ITM is Osaka Airport).

I prefer not to take a bus if I can help it, since I tend to get carsick if I'm not in the very front. So I've been leery of flying in to HIJ, since it looks like a bus is the only option to get to Hiroshima. But now that I study the Japan Rail search site, it looks like from either ITM or HIJ one needs to take a bus to get to the train station. Or maybe a cab, I suppose, but how much would that cost?

Sad about your flight getting in too late for same day connections by plane. HIJ is sadly is in the sticks (actually on the top of the mountain) and like most Japanese airports it is situated far from the centre. If you are apt to get "car sick" then the train-train combo's from NRT to Hiroshima via Shinagawa or Tokyo stations are very good options. If you would rather fly by plane then the FUK option is not so bad since it will not involve long transfers by bus. The subway is in the basement of the domestic terminals at FUK and it is only 2 stops to JR Hakata station (250 Yen). From JR Hakata to Hiroshima is approx. 1 hour on the Nozomi shinkansen !

ITM to JR Shin-Osaka would be about Y4000. Should be either taxi stand 1 or 2. There is a way to get to JR Shin-Osaka by train but your will have to transfer twice, monorail + subway + a short ride on the Osaka-Kyoto line.

I think train+train via Tokyo or Shinagawa is best.

That sounds very convenient! Unfortunately, if I fly SAN-LAX-NRT-FUK, I get to FUK at 10 PM, which is too late to then try to get to Hiroshima I think. If I fly SAN-LAX-NRT-ITM, I get to ITM at 8 PM, which should allow me to get to Hiroshima before 11. I think this is the only way to avoid an extra overnight. (The other way would be to fly SAN-ORD-NRT-HIJ, since the ORD-NRT gets in early enough to connect to HIJ, but going via ORD costs more.)

Train via Tokyo requires an overnight in Tokyo, I think. So maybe SAN-LAX-NRT-ITN, then taxi to Shin-Osaka, then train to Hiroshima.

From ITM to Shin-Osaka, a ride on MK taxi can save you some $. They estimate 3200 yen while other cabs quote 4180 yen. (Toll excluded.) You can also book one of their hybrid vans in advance with extra 1000 yen.

http://www.mk-group.co.jp/airport/index.html

There's a 490 yen bus that goes straight from ITM to Shin-Osaka every 20 minutes. By train there's just one transfer--you take the monorail from ITM to Senri-Chuo, then change to the Midosuji Line (aka Kita-Osaka Kyuko Railway on its north end) which goes straight to Shin-Osaka. Still a pain in the butt, though.

I missed that stop at Shin-Osaka but the transfer at Senri-Chuo is a long walk.

Like I said before, as long as you make the train by about 6PM at NRT, you can get to Hiroshima by mid-night. Transfer at Shinagawa is a bit easier. Just tell the JR counter staff you want to transfer at Shinagawa.

Remember to pickup dinner at Tokyo or Shinagawa. I like bento from the station better than on the train.

For the return, it sounds like flying out of FUK would be better than HIJ, since it's about the same amount of time and doesn't require a bus or taxi. Is that right? I may fly to HND and overnight there (or maybe even one extra day) before taking NEX to NRT.

HIJ is located in the mountains, accessible by car and bus.
http://www.hij.airport.jp/english/access/now/index.php

You can take the bullet train to Hakata in about an hour. Then subway is 5 minutes to FUK from basement.....

You must really hate the bus !

Bus or taxi from Shiraichi station is less than 15 minutes.

I think Itami is the go. Also you'll be landing there at night which is a pretty cool experience. Awesome in fact.