I fly Aer Lingus all the time (at least once or twice a year for several years) and they are fine - as good as any other airline. And almost always significantly cheaper.
The problem you may be having with certain cities is that while Aer Lingus flies to them, the timing may not be such that you can make a connecting flight. For example, from Dublin the only direct flights to the US are NY, Boston, Chicago, Hartford and maybe one or two others. For everywhere else you have to connect, and use a partner airline. On the European side, they fly to many cities all over Europe, but for example, the flight from Venice to Dublin gets in too late for you to connect to the flight from Dublin to Boston (or where ever). So while you can see that the various cities you may be interested in are places they fly between, the times don't work. There is only one flight a day from Dublin to each of the US destinations. So, another example - my closest airport is Hartford. Aer Lingus flies to Hartford, and to Venice. But the Venice flight gets to Dublin too late to make the Hartford flight. However, it does get there in time for the Boston flight. So when you first start looking it appears I could fly from Venice to Hartford (via Dublin) but when you go to actually book it, you can't.