Despite what others say the closed Italian is not the simplest opening to teach (or lacking in "openess"). It can be when both players are mindlessly playing standard developing moves, but there are some definite important points which are handy when you want to teach (or learn) about openings.
Firstly, keep your centre pawns safe. Ie keep an eye out for Nxe4 like in your line
Secondly, castling. Castling is good but not always. It can also serve as a base for an attack check the game Dubois-Steinitz.
Thirdly mindless developing. Mindless developing gets you nowhere because you will lack a plan. In the closed italian playing c3 and d4 at some point is necessary to gain something. For that reason check some games by Canal (he got Tarrasch and Capablanca in trouble with this line).

Thing is those issues are much clearer with this opening than with most others to demonstrate. As soon as you have a little feel for the play you should move on though as I agree that it can become boring to play this line (it is called the very quite game after all). Just move on to the Ruy with d3 or the main lines of the Italian at that point.

BPaulsen is right that for low-rated players, good understanding of principles is more important than any amount of opening theory.

What systems to teach young players is a very vexed question on this website, but as a longtime coach of young and improving players, I definitely would not encourage them to play into closed positions, and that includes the "Closed" Italian.  I'll say no more here, because this is not the right forum for this subject.  If you go to "General Chess" however, you will find lengthy discussions there.  Or by all means, start a thread there and we can have the same discussion all over again.

I teach my chess kids that 4.Bc4 (or 4.Nc3 in reaction to 3.Bc4 Nf6) is a suboptimal move, because it lets Black wipe out White's e-pawn at no cost.  Black is then left with the only pawn in the center.  It's true that 4...Nxe4 5.Nxe4! d5 6.Bd3! dxe5 7.Bxe4 is about equal, but Black is doing quite well with 7...Bd6.  Obviously he would like to get ...f5 in at some point.  He is definitely better than he was in the initial position, so in that sense, 4.Bc4 was a mistake.  Besides 7...Bd6 Black also has the diabolical 7...Ne7 (as recommended by Al Horowitz), which in contests between lower-rated players will almost always win a piece.  But even after 8.c3 f5 9.Bc2 Ng6, Black is O.K., so it's a trap sometimes worth setting.  

As pointed out by someone else, you're quite mistaken about 5.Bxf7+ Kxf7 6.Nxe4 d5, which allows Black the two bishops and utter domination of the center in exchange for very slight inconvenience with his king. For example, 7.Nfg5+ Kg8 8.Qh5 Qd7! is very good for Black.  You're also mistaken about 5.Nxe4 d5 6.Bb5, because 6...dxe4 7.Nxe5 Qg4 is advantageous for Black, as analyzed in the 1916 edition of the Handbuch.

The best fourth move for young players with both sets of knights out is 4.d4, and that is what I suggest you teach to your students.  To reach the Italian, the best time to play Bc4 is on the third move, after which 3....Nf6 4.d4 and 3...Bc5 4.d4!? lead into the kind of positions that I would prefer to see my own young students playing.  Once a young player has some sophistication, he could also consider playing the Evans Gambit.

Having said all this, there is one little wrinkle, and that is 4...Nxe4 5.0-0!?, an interesting gambit that perhaps produces enough compensation. Black can then consider keeping up the tension with 5...Be7!?, but it's probably better to accept the pawn and defend.  

Lee wrote on 06/11/09 at 07:08:38:


White's goal should be to get something more than that equal position after 7. Bxe4.

4. Bb5 runs into 4...Nd4! 

Closed Italian Game is the easiest thing to teach, and it's not violating any principles. There's also no craziness that can be used to throw white totally off.

After 4...Nxe4 black is at least equal.

You're better off just teaching them the Closed Italian Game (1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3).

I've never been a fan of teaching 1200s to just senselessly bash out developing moves. It's better they learn how to develop their pieces with a plan in mind, and the Closed Italian Game offers plenty of different plans.