Denver has a cryptic way of naming neighborhoods. Find one of the real estate maps that names the neighborhoods to help you. Based on what you are wanting, you can basically draw a circle with a 5 mile radius around downtown, and rule out the places you can't afford. Start by ruling out Cherry Creek .

Highlands is pretty cool these days and still has some affordable housing. If you are renting, go for Capital Hill. You will be close to everything and it has the most rentals, many in cool older buildings. I live in South City Park, and Colfax keeps it a bit more affordable, but houses still start at 300K and climb from there (Denver isn't the cheapest town). There are some rentals out this way as well. We are 2.5 miles from downtown, with lots to do on Colfax as well.