Arcadia is an easy drive to Pasadena. Hotels there will be full up soon, if not already.
Well worth it to connect and fly into Burbank. Yeah you are blowing an hour for the connection, but saving an hour and a half shuttling to car at LAX, picking up car and driving an hour or more in traffic to Arcadia. Burbank airport to Arcadia is just two turns onto the freeway and then a 20 minute freeway shot. Depending on when your departure is, LAX can be a nightmare to get to for your flight home.
I believe that there is metro/train service from the Arcadia end of Pasadena into the parade. I'll try to find out more about that. Are you buying seats at the parade or just going to stand on the sidewalks? Because one tip is to wait until about 15 minutes after the parade starts , and then journey to Pasadena. Take your place nearer the END of the parade instead of the beginning (it is about a 2 hour parade route, miles long). You will avoid all that early traffic getting to the parade. Wilson Street is a good place to shoot for/ that intersection. Homes all around the area offer $10 parking that morning, there is usually nothing else available.
Depending on what time your return flight is out of Burbank, you might want to choose to stay in Burbank or Glendale instead of Arcadia. If it's a weekday/workday.....Arcadia into the city can be a slow mess until 10am.