After 1.e4 e5, my first preference is 2.f4, but on when I from time to time play 2.Nf3 and face the Petroff defense, I like the plan with 5.Nc3 and long castle, simply because it's not as dull as some other lines of the Petroff defense. Generally speaking, I play the King's Gambit 2.f4 because it does not allow namely the Petroff defense and is more dynamic. But tastes differ, of course.
Help with Petrov's Defence Please

Actually, there are not 3 but, at least, 6 good continuations:
- Classical Attack 5. d4
- Cozio Attack 5. Qe2
- Nimzo Attack 5. Nc3
- French Attack 5. d3
- Kaufmann Attack 5. c4
- Millenium Attack 5. Bd3
I'd try all of them in different games. Well, Cozio attack seems to be really drawish.

I would agree also that Petrov's defense is just plain boring, but if you are looking to spice things up a little bit, you can always play 3.Nc3 and go into a three-knights game. However that does offer black more chances, and the opportunity to play the very dull four-knights game. You could also try not taking the e-pawn and try something more like a center game style (3.d4) or an italian style (3.Bc4).

Actually, there are not 3 but, at least, 6 good continuations:
- Classical Attack 5. d4
- Cozio Attack 5. Qe2
- Nimzo Attack 5. Nc3
- French Attack 5. d3
- Kaufmann Attack 5. c4
- Millenium Attack 5. Bd3
I'd try all of them in different games. Well, Cozio attack seems to be really drawish.
What is your goal as White: to play for a win, or play for a draw? That largely determines the answer. As Smexypapayas pointed out, you can bypass the Petrov entirely with 3. Nc3, which is the Petrov Three Knights Game, often leading to the even more drawish Four Knights Game. For a draw, that's probably your best choice. Other good choices for a draw if you want to continue into Petrov's Defense:
The Cozio Attack leads to an early exchange of queens, which is drawish.
The French Attack is very symmetrical, which is drawish.
Everything else listed is good for a try for a win. It just depends what kind of drawbacks you want as White:
From within the main line:
The Nimzovich Attack gives White doubled pawns when Black exchanges knights.
The Millenium Attack misplaces the bishop for a while.
The Kaufmann Attack typically gives White an isolated d-pawn.
Usually any main line, in this case called the Classical Attack, is the main line precisely because it's considered the strongest line, which is why it became the most popular.
The Modern Attack is also good for winning ambitions, and deviates from the main line early: 1. e4 e5 2. Nf3 Nf6 {Petrov's Defense.} 3. d4 {Modern Attack.}
1. e4 e5
2. Nf3 Nf6 {Petrov's Defense.}
3. Nxe5 {'Perigal Attack.' #1 pop. n 42%. 58% decisiveness. hoping-for 3...Nxe4?!}
3. Nc3 {Petrov Three Knights Game. #2 pop. w 40%. 72% decisiveness.}
3. d4 {Modern Attack. #3 pop. w 41%. 64% decisiveness.}

First of all, there is a whole world of interesting and sound variations if you decide to play 3,d4 instead of 3.Nxe5. Secondly, you are not a Gm or an IM, neither am I, neither are 99% of the players on this site. The fact that an opening has a drawish reputation at the grandmaster level should mean nothing. Almost all the pieces and pawns are still on the board! There are plenty of opportunities to spice up the game if you want to. There are no "drawish" openings at our level
Ok course you are right. Actually, this question comes from an OTB game I played yesterday. I played the drawish 5. Qe2 (cozio) line only for my opponent to make a massive blunder that led to mate in 1.
Just pick a line that is relatively sound, go through a bunch of games and then play it. The Kaufmann Attack, 5. c4, has worked well for me. Amongst other things it opens up the d1-a4 diagonal for the Queen. For many Petrov players it's a different game then they were counting on.
I don't face the Petrov very often in OTB play, so it's not worth spending much time finding the "best" continuation. Just finding a variation in which I'm comfortable.

The Cochrane gambit looks like it could catch a few players out at the lower ratings!
Lots of little traps here!

The Cochrane gambit looks like it could catch a few players out at the lower ratings!
Lots of little traps here!

I played the inferior move 3. Nc4 to get out of book(surprising, no human has ever played d5 after Nxe4). Now I play 2. d4 to prevent the Russian altogether. There are many options, perhaps you should tell us what kind of game you would like to reach. This is the variation I would play.
Queen side castling, both bishops pointing toward the king, and an easy pawn storm.
Possibly helpful:
Playing 1.e4 - Caro-Kann, 1...e5 and Minor Lines by John Shaw
http://www.qualitychess.co.uk/ebooks/Playing1e4CaroKannandothers-excerpt.pdf
My First Chess Opening Repertoire for White by Vincent Moret
https://www.newinchess.com/Shop/Images/Pdfs/9033.pdf
https://www.chess.com/article/view/how-to-understand-openings
A SIMPLE CHESS OPENING REPERTOIRE FOR WHITE by Sam Collins
http://www.jeremysilman.com/shop/pc/A-Simple-Chess-Opening-Repertoire-for-White-76p3916.htm
http://www.gambitbooks.com/pdfs/A_Simple_Chess_Opening_Repertoire_for_White.pdf
So my main options are the main line 5.d4
The queen exchange and drawish variation 5.Qe2
Or the interesting 5.Nc3 with the idea of castling long after the Knight exchange and a kingside attack.
I cannot decide the best course of action.
What would you play? more importantly, WHY?