There are lots of coffees out there. Some good, some awful. I realize that good and awful are very subjective terms. Everyone judges coffee differently. I judge coffee primarily on value (what am I getting for my money). So some people may think that good coffee is free coffee. Typically, free coffee is only good for keeping your heart beating.
If you have choice, you should brew fresh coffee. I prefer to brew manually in the V60. I have yet to find a brew method I like more than this for both brewing and drinking. When I brew in the V60, here are the top 3 things I'm looking for in an awesome cup of coffee:
Roast - There are 2 ways that I look roast. One is in purchased coffee. I like medium roast coffee, so I am building assumptions on what to expect based on the flavor description and the color of the bean.
Another way that I analyze roast is when I roast coffee at home. There are beans that build in temperature consistently and some progress nicely. I use an air popper so it is hard to get multiple batches all to a similar/consistent roast level.
Bloom - The bloom is my favorite part of brewing. This is the pre-wet stage of brewing. The water is kind of prepping the grounds to let go of tasty solubles. The grounds release stored carbon dioxide. That gas is what makes the bed of coffee grounds rise into a dome. I love this part because it is like an aroma explosion. I brew at my desk and people from 4 isles down will come looking for it, thinking its caramel or toffee.
This is also how I judge freshness. When all that carbon dioxide is gone, it is a safe bet that your coffee is stale. I did have some coffee from Perfect Coffee (now purchased by Blue Bottled) that was surprisingly full of flavor despite not blooming at all.
Flavor Over Time/Temperature - One of the things that makes a coffee truly awesome is the ability to enjoy it at different stages. I'm not gonna lie, when I spend a lot of money on a cup of coffee (or beer, or wine) I tend to nurse it for the whole day. So I like coffees that taste different as the temperature drops. For example, I roast a Colombian coffee that has a lot of chocolate and a little acidity when its hot; but as it cools, the chocolate moves to the back and the tangy acidity moves to the front. I enjoy this cup over and over again. I find that I will go to a meeting and come back to my coffee, take a drink and go, "wow, that is a Damn Fine cup of coffee."
Those are the three criteria that make a coffee really awesome in my book.