Stay in Little Tokyo, a low-rise, increasingly residential, pedestrian friendly neighborhood of Downtown LA. Perhaps the Miyako Inn. Walk a block to the Gold Line station, and take the Gold Line light rail to all the events in Pasadena. It is about a 25 minute ride, runs like clockwork, very safe and clean, and they run extra trains and late hours during the New Year holiday period. This is probably the easiest and most tranquil way to go, and Little Tokyo puts you quite close to Pasadena, with a short ride in.
Of course, you can stay elsewhere in the LA area, and either take transit (depending on location) or drive in. Traffic will be VERY heavy in some locations, so if you decide on this option, check back with this forum for driving and parking suggestions once you start planning where to stay.
No need to do a group tour. I'm not sure why anyone spends the extra money unless they are very cautious and inexperienced travellers, or have health and mobility issues (in which case it might be helpful).
If you are trying to save money, be aware that grandstand seats are not neccessary, and are quite expensive. Educate yourself about the location of the grandstand seats, too. The primo ones near the corner of Orange Grove and Colorado are expensive, but worth it if you want to be in the very best location, near the tv cameras. However, there are grandstand seats all along the 5-mile parade route, and in my opinion there is no particular value to many of them, unless you must sit down. You are seeing exactly the same parade as the folks on the sidewalk, just from higher up (and farther back). Watching from a spot on the sidewalk east of Old Pasadena just requires getting there by @ 7 am, to be sure of finding a great spot on the sidewalk with not too many heads in front of you.