You initially posted in Travel wanting to know the options available to you. You were referred to Expats (here) because among the options available to you are the EEA/EU and UK family formation/family reunion routes.
The EEA/EU route is available because your boyfriend is an EEA national and hence enjoys freedom of movement. For this option to work you will need to get married (or live with him for two years - just seeing each other as often as you can will not work). Once you are married you can approach any UK issuing post and get an EEA Family Permit.
The UK route is a bit more cumbersome, but you don't have to get married right away. Depending upon how long your boyfriend has lived in the UK, he may be eligible for a concession. The concession allows him (as an EEA national) to sponsor a fiance under the British rules. The visa lasts for 6 months after which you are expected to leave or get married at a UK registry office. They do not like to 'renew' fiance visas if there's a way to avoid it.
A fiance visa application under the British rules attracts a hefty fee; the EU application is free.
You can also try for any of the other economic routes like student, work permit, entrepreneur, and so on.
Those are the routes available to you that are topical for the Expats site. Further questions on those options should be taken up here as NEW questions.
There are also visitor routes available to you and questions about those should be taken up at the Travel site as NEW questions. I think your refusal is a mild one and can be possibly fixed with the right sort of attestation. Moreover, I doubt that a ban will happen if you use a member of the UK Law Society to represent your next visitor application.
For reference purposes and to clarify some of the comments, here's a screen capture of the relevant page of the application form about who the applicant knows in the UK....
Where 'lived with' = cohabitation at the same home address (the OP has not been living with her partner, but merely visiting).
There are no other such pages. Related pages will ask for names of sponsors however, but these are not necessary if a sponsor has not been declared.
For completeness purposes here is a screen shot of all the related questions. It is taken from the application summary page near the end...
Based on the form and what the form asks for, it's not clear at all that the OP failed to divulge something.