The two regional exploration of Kanto and Johto was something I love doing. To bad they didn't do the same for Hoenn to Sinnoh or Unova to whatever the next Generation would be. I say this Generation is very much the most favorable due to this reason mostly. The 16 gyms are insane. Although in Kanto, they are all surrounding the levels 50-60ish. All you need is a Pokemon beating the Elite Four over and over and over again to level 70 and you can just blast on by the Kanto Gyms. Plus I feel like as long as Johto is, they should had done a bit more with Team Rocket when visiting the Kanto region, rather than just that one guy in Cerulean City.
The Bug Catching competition was fun as well. I loved doing that. Although I do happen to release those that I did not want after the competition. Does that make me a bad trainer for letting those Wild Pokemon back into freedom rather than slaved into my PC?
Let's not forget the HeartGold/SoulSilver games of Pokeathlon Dome. That was a fun place to attend. It definitely reminds me a lot of the Mario Party memories :D