The best replacement for canon sx500 is nikon l820.

The best alternatives to canon sx500 are rated as following:
★★★★★  nikon l820
★★★★★  sx50
★★★★★  nikon p510
★★★  nikon p520
★★  nikon l810
★★  nikon l320
★★  sony h300
★★  sony h200
★  nikon l830
★  sony hx300
★  fuji s8200
★  canon sx50
  canon sx260
  sx260
  nikon s9400

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Speaking about canon sx500, one probably shouldn't forget about nikon l820.

Other search terms related to canon sx500 and their ratings are:
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