Here's a list of characters who are not romanceable yet but will likely be in the future.

Roxxy

Roxxy is the school's popular cheerleader archetype and polls on the Patreon indicate she should be getting an update so players can interact with her more in one of the next updates.

Eve

Eve is the goth/punk/emo girl from school and although she crops up in a bunch of quests including Rap Battles she is currently not romanceable.

Grace

Grace is Eve's sister who runs the Tattoo Parlour Sugar Tats and will likely be a branching arch from Eve's romance much like Mia and Helen's storylines.

Rhonda

Rhonda is the school's athletic track champion who promises to train with you if you can pass gym class. As gym class has not been implemented yet the same is true Rhonda's character arch.

Kevin

You can unlock Kevin to help you with your Stats training to increase your strength but he is currently not available to do anything else with despite being the only obviously gay character and also being on your checklist in your locker.

Anna

Anna is tied into Mrs Johnson's storyline and you can practice Yoga with her in the gym but can't currently go any further with that quest branch.

Currently, there is only one obvious class which hasn't been added to the story.

Gym Class

While gym appears on your report card there isn't any way to progress with this storyline just yet. Even if you have your stats maxed out you currently can't pass the gym test and raise your grade.

Beach House

The beach house can be purchased but you can't live in just yet so it's currently a waste of your hard-earned money.

Beach

Nothing can be done here yet.

Warehouse

Despite being told to meet the thugs at the warehouse during Debbie's Storyline, this area is currently under construction. 

In Summertime Saga you'll need to collect three stacks of magazines to finish the Art Class and Miss Ross Quest lines. This page contains the locations for these magazines and how to get them.
For each Magazine, you'll need to have raised your Stats to be able to collect them.

Find the first stack in the teacher's lounge on the second floor at school by talking to Miss Dewitt and having high enough intelligence to answer her question.
The second you can get at the basketball courts but you'll need to have the dexterity to slip away from Dexter.
And the third you can get from Kevin in the Cafeteria if your charisma is high enough.
Back at art class you and Mia can go ahead and make your collages which will end class for the day.

Summertime Saga has a lot of interwoven story-lines and requirements for passing those, so here's a list of things to do as soon as you can to make these things a bit easier.

Get The Master Key

During Day 1 you'll make note of a master key and you'll find several quests will require you to have it on order to finish them.
To get the Master Key head into Mrs Smith's office on the 3rd floor at school during the afternoon. Usually, her office will be empty and you can go into her desk to get the key.

Fix Your Computer

The computer in your room is broken and you'll mention this to Erik at the end of Day 1. He'll tell you to buy parts for it at ConsumR at the Mall. It will cost $200 but it's a good idea to do this ASAP.
Not only does your computer allow you to train intelligence it's also required to study for French Class as well as complete Jenny's storyline.

Unlock Stat Training

Stats can also lock you out of being able to complete a quest, so make sure you've unlocked all the stat training possible by checking out our Stats page.

Buy a Bicycle

Working in Diane's garden is fine but you can make a lot more money delivering pizza once you have a bicycle.
Check your mailbox to find the advert to unlock the Pizzeria and then save up the $500 required to get the bike for much faster cash.

Progression on certain stories will often be locked behind the passing of time. If you can't seem to get the story you're working on moving then try something else for a while and make sure to sleep. 
Sometimes things may require the passing of a full day or even the weekend to pass. Don't assume the game is broken before letting sufficient time pass to find out. 

Summertime Saga is still being developed and worked on which means that some quest lines are unfinished or simply unavailable. If you're stuck it's a good idea to check in and make sure what you're doing is even finished in the version of the game you're currently running.