I'm guessing you're looking for something kind of fresh and summery pop with a bit of a hip-hop bounce to it? Here are my picks, although I'm not totally sure if this is what you're looking for. Generally, I'd reccommend her 2nd full Korean album "Nûl.. NO.1" and her 3rd full Korean album "Atlantis Princess" to you.

Shine We Are! - Similar to Atlantis Princess, very cheerful and summery, but with a bit more funk to it. A little 70s. Also one of my favorite BoA songs (released on my birthday!).

Earthsong - The B-side to Shine We Are!, and it suits it. A bit poppier, less laid-back and fun though.

flower - A really cool mid-tempo. This is a really nice song to drive to with the windows down and a nice breeze.

B.I.O - Really fun, energetic, sexy beat. I'd like to see this number live, it just has cute-sexy energy, and the "Communication" line gets me every time.

Milky Way - Korean version has a better flow to it. It's poppier than some of the other songs, but it still has that summery feel to it.

NO. 1 - The more popular version fits what you're looking for, I think. It's more extroverted, whereas the original version found on initial pressings of her 2nd Korean album has more of an introverted hip-hop flavor.

Amazing Kiss - If the two songs you mentioned were day, this song would be night. It's very twinkly-stars-in-the-night-sky, but has a great beat, an excellent melody, and it's very fresh and clean. My favorite BoA song.

Midnight Parade - Really hot beat, as far as BoA goes. Another night time song.

Dugûn-dugûn (Pit-a-Pat) - A soft, clean beat.

My Sweetie - Fresh and cute, along the lines of the previous song, with a fuller sound.

Shy Love - Much like My Sweetie.

Easy To Be Hard - Has a bit of a late 80s, early 90s feel to it. Cheerful, cool beat. Not my favorite, but still a good song.

Etude - Reminds me of Atlantis Princess a lot somehow. Maybe a little girlier in the arrangement, just more twinkly sounds and has a soft feel despite a really cool beat and energetic vocals.

My Boy - Very summery. In fact, it was on an SM Town summer vacation album. Catchy-as-hell chorus, and the song builds really cool.

LA-LA-LA LOVE SONG (w/z SOUL'd OUT) - A little like "the love bug", but much more disco-y.