Get the Rest of the Gym Badges.
Latias, being found in Pewter City, is captured long before the game is completed. As such, there's much left of the Kanto region to explore, notably the last seven gym badges in the region. Pewter City's Gym Leader, Brock, will give the player a run for his money while the next leader (Misty) is sure to topple fire Pokemon with her water-based strategies. Continue until the last badge is accquired in Viridian City.
Find the Legendary Pokemon of the Region
The legendary birds, unlike the Generation I remakes and originals, are in different locations throughout Kanto. Moltres is now deep within Mt. Silver, for example, instead of on Victory Road. Zapdos is on Route 10 and Articuno is in the Seafoam Islands. Mewtwo can be battled and captured in the Cerulean Cave, next to Cerulean City, after the eighth Kanto gym badge is accquired. It is at Level 70, so be prepared (a Master Ball helps).
Defeat the Elite Four and Kanto Champion
The Elite Four of the Kanto Region consists of the same four trainers as in the Generation II games. Will, Koga, Bruno and Karen will each test your strength as a trainer in tough one-on-one battles. Will has psychic Pokemon, and watch out for his powerful Xatu. Koga's poisonous team, lead by an Ariados, can do some serious damage without Antidotes in hand. The Hitmontop that belongs to Bruno will kick the player to a blackout if weaknesses aren't exploited. Karen, the Dark opponent, won't hesitate to sick her Gengar on unsuspecting Ghost Pokemon. After defeating these four, face off against Champion Lance and take his dragons (like Garados and Charizard) out with Steel Pokemon.
Battle Pokemon Trainer Red
Red, also known as "Ash Ketchum" in the anime series, was the first protagonist in the Pokemon video games series. He is a powerful trainer that stands atop Mount Silver, waiting for anyone to challenge him. His team captain is a level 88 Pikachu, which is supported by a level 84 Blastoise, Charizard and Venusaur. His level 82 Snorlax and 80 Lapras bring up the rear of the team, making for a well-rounded team. Play on their weakness by sending out Pokemon that prey on each respective type (such as Latios against Venusaur). Take a lot of Hyper Potions in the battle, as you'll need them.