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I usually do weights (including abs) and cardio training on different respective days. Obviously, when I do them on the same day I do weights first, but I was wondering whether it would make more sense to hold off on the abs until after my run, or to keep it together with the other anaerobic exercises?

I don't think that it makes much difference. Most ab work is geared towards conditioning and defining, not hypertrophy. Keeping your abs tight while you run is a good ab workout in itself, so consider reducing or even eliminating your ab work on days that you run.

What specifically is your ab routine, and are you working hipflexors as well? For me, I usually do abs after lifting weights, then grab a quick carb drink or gel, wait about 10-30 mins depending, then go run. I usually try to get sometype of energy source between working out and running as I am usually smoked and have little to no energy left after anaerobic exercise. Just remember to give your abs some recovery time as well, I see alot of people doing ab exercises everyday, which isn't really a smart thing as they are still a muscle that needs recovery time.

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I split my 'ab' routine into 3 days usually: rectus abdominus, obliques, and hip flexors and I just rotate through them (hiting transverse abdominus when I think about it) and it works fairly well for me (sixish pack). On cardio days I prefer to do abs afterwards just because running is quite taxing for me (esp if I'm doing any HIIT) so it is too much to have my core fatigued before I even start.

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Sounds like a pretty solid routine to me. It's pretty much the same system we used when I was in the military. Go for it.

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Don't forget to swim! You'll thank me later in life...