Just continue with 2. Nf3. 
From King's Gambit.
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King's Gambit should be fine, so long as you don't get your king in a terrible position. You could try Ruy Lopez.
I like the King's Gambit. Most players say no however and advise playing 2. Nf3 going for a Ruy Lopez because it's more sound. That may be the case but there's a ton of theory to know with so many possible defenses to the Lopez. Also playing 2.Nf3 someone playing White has to be ready for Petrov's Defense as well which requires some more study time. Probably more theory to memorize with 2.Nf3 than 2.f4 and you'll never surprise anyone playing 2.Nf3, but you might with 2.f4. So there's my case for the King's Gambit and why I play it.
Several openings suggestions in my blog.....(including King's Gambit)...
https://www.chess.com/blog/RussBell
In particular, since you are a King's Gambit player, you might like to give the Vienna Game & Gambit a try. After 1.e4 e5, by introducing 2.Nc3 prior to 3.f4 it is considered an improved version of the King's Gambit. The point being to first establish increased control of the center by protecting e4 and adding a second defender of the central square d5. All of this in anticipation of initiating an attack on the kingside beginning with the move 3.f4. The opening is very popular at the amateur level, and playable even by advanced players.
https://www.chess.com/blog/RussBell/introduction-to-the-vienna-game-gambit
For more opening suggestions check out the chess openings tier lists videos by GM Hikaru Nakamura and IM Levy Rozman...
https://www.youtube.com/results?search_query=chess+opening+tier+list
For beginner-intermediate players I also suggest to check out GothamChess (IM Levy Rozman) on YouTube for recommendations and quick tutorials on openings....
https://www.youtube.com/watch?v=NFod-ozimmM&t=103s
https://www.youtube.com/watch?v=Qdyik5UwBtM&list=PLBRObSmbZluTpMdP-rUL3bQ5GA8v4dMbT&index=8
Can somebody suggest to me an opening for e4 e5. I am currently playing king's gambit.