One, this was really sweet, awwwwww
Two, I'm assuming your ire towards "Romeo and Juliet" comes from experience with poor teaching of the material. And for whomever needs to hear this- ROMEO AND JULIET ISN'T A LOVE STORY/ROMANCE IT'S A TRAGEDY! Annabeth's teacher is wrong. The whole point of the miscommunication is that it ends horribly. Why am I so worked up? I love Shakespeare, and EVERYONE'S first impression is, "that love story that ends horribly." There may be romantic elements, and the tragedy is based in romance, but Annabeth's right-it's not a functional romance. But it's not supposed to be presented as such. Thank you to you eyes for their service in reading my rant.
Have a lovely day!

Great job! For a story tagged as "Tooth-Rotting Fluff", it provides a lot of material to chew on.
Going into an in-depth analysis:

TONE
This piece (fluff notwithstanding) is gentle and humorous, in true Riordan fashion. It is somewhat of a departure from the great tension in HOO (and TOA), but it is refreshing to see our characters at peace.

PERCY
Percy's character traits are his kindness, humility, sense of humor and lack of self-confidence. These are clearly shown throughout the story.

I recognize that "Percy looked the way he always did when someone complimented him ... qualities." is written very similarly in Nightmares, Chapter 4. Just wanted to point that out.

My only complaint is that Percy may have seemed a bit too perfect, though this might be a side effect of reading in Annabeth's POV. Also, he really wanted to make up for what happened in the month's anniversary.

ANNABETH
Annabeth's POV reveals her complex personality. While an analytic thinker, she is also excessively prideful (evidenced by her reaction to a humiliating defeat). She is also no-nonsense and impatient as in the line "considering killing her boyfriend and her best friend". Having been jaded in others in her life, she is amazed by Percy's excessive kindness.

SUPPORTING CHARACTERS
There is a whole cavalcade of supporting characters in this story, which lends it more flavor. I especially liked Piper's fun-loving personality (something we don't see too often in the canon because of her hardships), as well as Hazel and Frank in the new camp. (Seriously, these three characters suffer a lot during TOA!) I also liked seeing Percy's relationships with the others like Frank and Hazel. (In HOO after SON, there was a major focus on his relationships with Annabeth, Jason, and Leo.)

REFERENCES TO CANON
1) Fateful Meeting at the Porch
2) Circe's Island and Rescuing Grover
3) Percy sneaking on Quest and Holding Up Sky
4) Air Bubble
5) Traveling in Pacific Ocean
6) Walking through New Rome
7) Pit in Rome
8) "Baby Seal Eyes"
9) Piper's Advice Facing Mimas

The work references the canonical events/dialogue just in tidbits; it does not completely hash out events nor completely forget its roots. Such respect for the source material is rare indeed.

WORLDBUILDING
1) Camp Half-Blood: Capture the Flag, Counselor Table, Strawberry Fields, Climbing Wall, Big House, Naiads
2) Animals: Mrs. O' Leary, Blackjack, Peleus
3) New Rome / Camp Jupiter: Caldecott Tunnel, University, Fountains
4) Other: Atlas Statue, Door Of Orpheus

I love how the small Percabeth story fits into the larger picture; for pure fluff, this work has some strong world-building. I love how the some of the above details are repurposed to fit within the story.

OTHER DETAILS
1) Annabeth's "Romeo and Juliet" essay
This was hilarious and totally in character. (Having suffered through "Romeo and Juliet" as a high school freshman, I can relate to Annabeth's blunt essay. Well, not the deep sense of loss...)

2) Gifts (skateboard, puzzle, chain)
The gifts were especially creative. (While the chain may be cliched, I have no problems with it because of its intricate detail and symbolism.)

(INCREDIBLY) SMALL NITPICK
"Grove from Polyphemus" - "Grover from Polyphemus"

CONCLUSION
I really enjoyed this story because of the new elements it brings, seeing supporting characters in the gap between HOO and TOA, and (of course) some wholesome Percabeth fluff.

I don't usually leave reviews anymore. But this seemed like a perfect opportunity for an exception.

Percy s plan the story was perfect in contrast with Percy's actual plan which was flawed. And that was the reason the story is so good.
It shows how well they know each other, how they are still learning each other though. They love each other for exactly what they are and they took the time to get to where they are and that's why they are so comfortable.

I also loved the romeo and Juliet reference they got nothing on percabeth.

This is honestly SO BEAUTIFUL! I can't lie, though. I was expecting a proposal. But I'm actually glad it wasn't a proposal, because that would've been a little cheesy...
But anyways, I LOVE this! This is a very accurate portrayal of Percy and Annabeth's relationship. They were both so in character, and it was adorable how Percy forgot the time difference! One of my favorite Percabeth fanfics! Your fics never fail to put a smile on my face!

I actually agree with Annabeth on the Romeo and Juliet. Well not exactly her reason. I've always thought that the whole deaths could have been avoided if they'd just communicated with eachother. Or even just waited for a bit longer before making such rash decisions to end their life. I also don't like how it romanticises suicide. Everyone keeps saying how its the most epic love story but really not being able to communicate, being as reckless as they were, I feel like it was more of a lesson on what not to do. If Annabeth's english teacher doesn't realise that, then..tsk..tsk..

Anyways I loved the whole round up of their relationship. Can you believe it. Oh, it still hits so hard. 5 years of rivals to friends to best friends to not talking to romantically involved. Just a rollercoaster of ups and downs and choices and they still came together. Its why I love Percabeth so much.

Lovely gift idea from both of them. The two-in-one jigsaw, the skateboard, the necklace and around the world trip. So thoughtful.

Awesome! So sweet Percabeth!

This was adorable. I smiled the whole way through. My favorite part honestly was meeting at the porch because that is where everything started. That and when Percy forgot about the 3 hour time difference. Anyways I really liked it keep up the good work.

I love that this is sweet and cute- but at the same time funny, adn in character and not cringey!
Percy is such a dorky cutie and this really shows that 3
I'm just gonna go sob into my pillowcase now bye

This was so sweet! I love this story and your writing! So soft and cute very in character! I don’t understand why people think that Percy would forget their one year or anything important to their relationship and Annabeth because he’s such a sweet boyfriend in cannon. Really love this story!