Your wheel (rim) could be damaged so you should have a tire shop take a look at it. You can probably get a tire for like $30+, and maybe $10-$15 to balance it. Try a used tire cause most tire places would suggest changing tires in pairs.
There are currently a number of HDHomeRun models on the market: a single-tuner ATSC/clear QAM model, a dual-tuner ATSC/clear QAM model, a dual-tuner commercial (TECH) ATSC/clear QAM model, a dual-tuner DVB-T/unencrypted DVB-C model, and a three tuner CableCard/clear QAM model.
The cheaper guitar-tuners only have notes EADGBE like a guitar. The chromatic tuner has all twelve notes of the scale, which makes tuning a half-step down or going into altered and open tunings easier. They're worth a few extra bucks. Un-plugged is not the same as never-was-plugged-in-to-begin-with.