It depends on what you consider onshore. Cyprus,
Hong Kong, and
Singapore can be considered both onshore and offshore. They are reputable jurisdictions and banking there is great.
Malta is another option, in particular
Bank of Valletta. I wouldn't recommend HSBC Malta. They barely work with local companies. Don't bother with other banks in Malta.
Kommerzbank and Deutsche Bank are known to deal quite a bit with offshore jurisdictions. It's possible they might consider a
Seychelles IBC. The same goes for Reiffeisen and ING.
It would help if you already have a long relationship with an offshore bank to use as a reference when approaching an onshore bank.
But please keep in mind that banks will decide on a case by case basis whether they allow you. While I know for a fact that Bank of Valletta has opened accounts for IBCs in the past, it might not work in your case, depending on your profile.
The question all onshore banks ask themselves when they are approached by an IBC is, "why is this person using an IBC?"