Well, that's why "look up the pitot to see if there are any bugs in there" is in the check list. Not that there's much chance of actually seeing them of course, so it's only going to catch some cases. Also of course part of the reason you check the ASI during the take-off run ... but in your case that was OK, you lost it on the climb.
People have killed themselves following ASI failure by getting the wrong speeds on the climb or on the base turn or wherever, followed by a stall/spin crash - that's the real danger. Which is why I do a circuit with the ASI covered up every now and then. Well done for avoiding that, which is the main thing to say about your experience!
So ... how to stay alive with no ASI? The climb is easy - full power, and you know what the picture looks like. The cruise is easy - you know what power setting you usually use in the cruise, that'll give you the same speed it usually does. The landing is more tricky - you have to go by the picture and the feel of the controls, and err on the side of being a bit fast rather than on the side of stalling out of the final turn and spinning and crashing. Personally I end up a bit fast, but safe; I wouldn't try a no-ASI landing somewhere with a minimum length runway, I'd divert somewhere where the runway length wasn't going to be an issue.
Oh, and the fire trucks? Y'know it only takes them fifteen minutes to read the paper each morning, and they're exceedingly bored for the rest of the day. I've had them called out at least twice!
I don't think you made any mistakes. The only real choice you had was whether to land back where you'd just taken off or whether to return to your home base. Returning to the home base seems to me to be the safer choice, as you're more familiar with how it should look and feel in the circuit at the right speeds - the cruise itself with no ASI is a complete non-event as you discovered, simply set the right RPM and there you are.