I considered making an odometer (simple counter) from calculator guts, a reed relay, and a magnet, and going full-on DIY cool with it. The extra math involved after every ride, the time it would take to construct mounts, and cost of components wouldn't be an efficient trade for a real speedometer.
So, I went and bought the first brand new thing this bike has (other than the original tube I replaced recently): A spiffy new bike computer. I know the Bell models have mixed reviews, but the Schwinn was out of stock everywhere; and this one was only $13. Being a tinkerer of all sorts, I figured any problems that may arise could be resolved. Some say the vibration of motor bicycling makes them useless, but I haven't had any problems with mine at all. I noticed a bit of wiggle between the mounts and the handlebars when I first attached it, so I placed some thin folded cardboard squares between the gaps. It doesn't lose signal, cut in and out, or move around like I've read of them. It wouldn't have been nearly as solid without something filling those gaps. This has worked well for my bike, anyway.
If you have one of these particular bike computers, try this before you toss it. Mine has worked for a mile and a half so today, at speeds up to 21 mph.
After doing some fast calculations, I've put no less than 10 miles on this bike doing my daily rounds since I built it. This doesn't include the distance run across town, either. I'd estimate that was at least another 3 each way. That's a good indication of longevity if I treat it right.