Is Antonio seen as a solitary and sombre character that audiences don't like?
I suppose Shakespeare created Antonio as a serious character since he should be the one in the drama who assumes a more responsible and caring role. He comes across as somber since he has business interests which he needs to protect and these, we know are at considerable risk - being a merchant who has his goods transported across capricious oceans would, I assume, cause anyone to be somber.
We also know that Bassanio is irresponsible and spoilt by Antonio's generosity, a trait Bassanio easily exploits. It may be that Antonio is so much concerned about Bassanio's well-being that this may also lead to his somberness. Antonio, is however an honourable friend, prepared to take risks in order to protect, help and defend those close to him.
It is ironic though, that Antonio despises Shylock as much as he does - I suppose one could attribute that to xenophobia and possibly some professional jealousy. It is clear that Shylock always has money (through his loan-sharking) and Antonio sees this as reprehensible. However, usury was a common practice at the time and Antonio has, after all, put all his eggs in a few very risky baskets. I suppose that that causes a great deal of anxiety - hence the serious mood.
Antonio can be perceived as being somber and it is never truly clear why he would feel this way. It may have something to do with the contradiction of his generous personality and his job as a merchant which is based on profits. He, therefore, might be conflicted in wanting to be generous while also needing to extract profits (an ungenerous practice) in order to stay in business.
Whether or not audiences like him depends upon the way the actor portrays the character. However, given that his generosity is a large part of his character and the plot, some or most audiences probably rally around him, as they do with Bassanio and Portia. Antonio is willing to sacrifice himself for the happiness of Bassanio. Audiences would find this admirable; although an argument could be made that Antonio does show some hypocrisy in condemning Shylock of usury (extracting high profits from debts). So, it really depends on the performance and the reader/viewer. Antonio has this one flaw but also expresses his generosity with his friends. Therefore, he can be admired and criticized. In general, he is perceived more for his generosity than his condemnation of Shylock.