I know what you mean - if I'm not in the right mood, starting a Pokemon game can be dull what with all the training up and having done it before.
I suggest set yourself 'training targets'. Like, you get the starter and say - "Right, before I get to Mr. Pokemon's house I'll be at Level 8." and then "Ok, before fighting my rival I'll make sure I'm level 10".
Then when you've gotten some Pokeballs from Elm's Aide catch one or two Pokemon you *know* you'll have in a fairly long term team (like up until they're level 30 or something) and train them up to the same level as your starter. Then train your starter to level 15 and have the rest follow suit.
I often find that keeps me playing for a couple of hours without me even realising how the time has flown by.
Which bits do you consider the 'boring beginning' bits?