General rules:
Working your arms all day will give you nice muscle definition, as a result, yes your arms will look better than say your gut.
However, the gut is unique. You could run sprints everyday, and you'd get some jacked leg muscles but your gut will still stick out if you had one to begin with. This is b/c the abdominal wall is completely covered in whatever fat you have there. So until the fat is removed, you will still have a gut, and your abs will not show.
Fat loss comes from diet and exercise. Calories in has to be less than calories out. It takes time, and it sucks. Once you burn it off, don't let it pile back up.
The best way to burn calories is sustain effort all day. Do light/moderate workouts multiple times a day(2-3x a day if possible). Pace yourself. Don't kill your muscles with lactic acid buildup early on. The key is endurance.
Generally, training starts with fat loss, moves on to cardio, then to anaerobic for the ring.
At the same time, training goes from low intensity, to moderate, to hard. See the pattern?
So start with some LONG low intensity stuff if you really got some serious fat to worry about, which I gather you don't.
Then move to moderate stuff like middistance runs. Swimming absolutely is kickass for this. Low risk for serious injury(except drowning death, heh).
Then the final stage is anaerobic.
For simply sustaining fitness, after you've really done some cardio, you should just mix the moderate/high intensity work to maintain both at the same time, and give training variety.
And ddrive is talking about an "elliptical." It's a good running replacement: only reason to stick with running would be if you actually WANT to be a runner.
And in the end, the hardest part is just getting off your ass and doing it. If you can do that, don't "sweat" it.
