For my fiance and I, these two topics went hand-in-hand.
You can't nail down a date until you know the venue works on that day. You can't nail down a venue until you know what day you want to get married on. It's a vicious cycle and it drove us crazy for two weeks.
Here's how we tackled it.
First, pick the season you want. We knew we wanted a summer wedding so we could have it outdoors.
Next, pull out a calendar and cross off all the dates you know do NOT work for various reasons (college graduation, HoopFest, family birthdays, etc., etc., etc.)
Then decide what day you want to get married on. Saturday is the biggest pick, but Fridays and Sundays are becoming more and more common for cheaper costs of venues. As you look at venues, you will need to decide which is a higher priority to you: the day of the week you have your wedding on, or the venue you have it at.
Once you consider those things, narrow down your dates to 3 and begin researching venues.
Now to be honest, I got completely overwhelmed and stressed out by venues. We knew we wanted a outdoor, country style wedding so I looked for ranches/barns/farms in the area. The places I found were either WAY too expensive, WAY out in the middle of nowhere, or had WAY too many rules.
The first problem is obvious. The second...I didn't want my guests to have to drive 30 plus minutes from their hotel to my wedding and I didn't want to have to travel far from my home either or to a hotel that night. The third problem is what really pushed me to the decision we ultimately made for our venue. Every venue had rules about capacity, parking, catering, rentals, and time allowed on the day. They were all so different and hard to compare.
My fiance and I ended up deciding to have our wedding in a family friend's backyard. They live on a farm and have a huge backyard where they got married themselves. The price: free. The location, 10 minutes from hotels that guests would stay in. The rules: drive slow to avoid dust and don't both farm animals haha.
So though I did not go the traditional route with renting a venue, hopefully these tips about choosing a date and a venue can help you in your wedding planning.