To unlock a city, you must complete every gig in that city. Each establishment will state the fan/star requirement to unlock as will each gig within the venue. If you become stuck, just search another city and play the easier venues until you meet the requirements.
Difficulty will not influence the amount of stars received, so you will want to play on the highest difficulty you are able to get the most stars. As you likely also want to hit 1 million fans play on hard when possible as medium will cap your fans at 550,000. Note that your fan capacity is determined by the lowest difficulty, so if you play bass at expert and vocals medium, your band will be scored at medium.
Unless you are one of the lucky players with someone to play co-op locally you will have to learn to play Vocals/Bass (Voxtar) as online co-op is not supported. This is the most popular method - head to your local music store and invest a few bucks into a mic stand or you can used the Xbox headset.
Some of the more exclusive venues have minimum difficulty settings, so start getting used to playing on medium, hard, expert. Memorizing the vocals and concentrating on the instrument is probably easiest. Considering you only need to pass the gig it is wise to reserve some overdrive power in case you need to bring the other back.
Keep a warm beverage handy to keep the vocal chords going – tea with honey or lemon is recommended by most professional singers, but use whatever suits you. You can hum to save air on the longer held notes. For the “talky” parts make sure to hit those consonants hard.