There are a few solutions that combined will help you arrive at the correct answer, but the most important thing to keep in mind is that you are in control of what the answer is. 

On paper: How does the home you are considering compare on paper to other homes? I'm talking about the number of bedrooms, bathrooms, size, lot size, age, garage size, etc. In every area different things can drive price, but no matter the area you have to compare apples to apples.

The Market: What I'm getting at with the market, is whether you are in a buyer's market or a seller's market. If a Realtor tells you it's neutral or stable you've got to believe that it's not in your favor, because if it was they would just tell you. If it's a buyers market and inventory is high you might be able to start with a lower price.

The Terms: I'll make this one simple... if you are a cash buyer who can close in 10 days without any contingencies, you've got a lot of control. If you're using FHA financing and the lender things it could take 60 days to close, those terms might not be very appealing to the seller so something else should be (the price).

Your Instinct: Here's one you rarely hear from a Realtor. Your instinct and/or gut feeling should play a role in what you offer. This is our opinion, but if the offer you make is based somewhat on what you feel the home is worth, you're going to feel much better about it whether it works out or not. You've seen other homes; you know how important getting THIS home is to you and whether or not you're okay if you don't get it. 

 Your realtor: There is nothing wrong with your realtor suggesting a price, as long as you aren't surprised by it. By the time you are ready to make an offer on a home, you should feed educated and confident in what you should offer. Whatever your realtor suggests should be close to what you are already thinking. If it's not, find out why. Maybe there is something you missed, or something the Realtor forgot to mention.