To the right of the town, there is a Route where trainers are. I used it for XP and levels. You can as well.
Also, if you go all the way through the trail and enter this house to get to Celdon City to get some items at the Dept. Store you'll need later on.
There's some items to pick up on this shortcut.
Now head up and to the left to get to the city.
Enter the big building that says "MART" and head all the way to the roof where the vending machines will be.
Buy any or as many drinks you want, but amke sure you have a couple for the guards at the actual ways to cities. They'll be thirsty and if you give them a drink, they'll let you through.
Also, there'll be a girl throwing a tantrum at the roof. Give her a drink and get a TM.
Head out of the city through the trail on the left to get to a house where'll you'll get Fly. NOTE: Before you do, head to the Game Cornor at the bottom of the city and press A on the poster. It'll reveal a secret hideout and you'll find the SIlph Scope.
There ya go!
Now teach it to your flying Pokemon (mine is Pidgey) so you can fly to any city you've been to. Very useful.
The TM you recieved back at the vending machines is "HORN DRILL". Probably the strongest move for your Nidorino.
Fly back to Lavender Town now.
Now head to the Pokemon Tower.
Go up the stairs on the right to head up stairs and eventually to the roof.
You'll meet your rival again. Just defeat that punk once again.
Now, continue going left and defeating the "Channselers" and going up the stairs to the roof.
Once you get to the last staircase, there'll be a ghost you can't ID. It'll be the Marawrak.
Now head up and you'll find Jesse and James. Defeat them.
After that, go talk to Mr.Fuiji.
He'll give you the PokeFlute when he takes you to his house.
Now head to Celadon City and head to the right.
Instead of going through the shortcut, go through the actual way to get city to city. This will take you to Saffron City.