Welcome to aikido, Dave!
Re: aikido and self-defense, aikido is great, but it isn't a quick path to mugger-proofing yourself. I'd suggest supplementing it by developing other skills such as situational awareness. I've never had to use aikido for self-defense, but situational awareness has gotten me/kept me out of problem situations many times. Aikido's the backup, so far my primary hasn't failed.
I couldn't agree with Mary more. It will most likely be years before you are skilled enough to use Aikido in a situation like you described. Situational Awareness is great but also the realization that your wallet and watch are cheap compared to getting seriously injured. I think you did great to come out in one piece. Good job and enjoy your path with Aikido.