They need to keep it modern for several reasons.
1. Most relateable to today's society. It appeals to the younger generations, as well as the old generations, in terms of tracks on the radio, and vehicles.
2. The smart phone and in game internet help keep the world feel like its alive.
BUT, I am not against the past. I think it can be done in a more interesting way. Basically, the story starts off in the past, like in the 60's, 70's, 80's, 90's, or 2000's. Something happens. IE, your character lays low for a few years/decades, goes to prison, play as the original characters son or something. The bigger the gap, the more interesting, but it can't be too big, due to characters aging. So in my book, mid 60's is as far back as you can go.
If the next GTA is set in Vice City, I definitely want to see the 80's. The fact that GTA VC, and GTA VCS was set in the 80's is one thing that made them so special. But, since the HD era GTA's benefit from being in modern times, I would like to see it during two different time periods. Story starts off in the 80's, and then about half way through, maybe like 40-50% of the way through, it moves to modern times, aka the year that the GTA came out.
Of course though, if they did that, I hope that the radio stations change in a way where I can still listen to the tracks from the 80's decade. So for example, if there is a pop station that plays the current music, it would play the 80's music in the 80's, then modern music in modern times. However in modern times, there would be another station added which has an 80's hit theme. It would play the songs that the current pop station played in the 80's.
Although, for the Online portion of the game, I guess that would just be set in the modern version.