Another idea just to throw out there, rent a vacation home that allows events.
Here is an amazing one with one heck of a yard for $200 night (starting).
http://www.homeaway.com/vacation-rental/p3000389HomeAway.com
VRBO.com
Of course you'll have to contact the owner to see if events are allowed. Some say they are, some you'd have to ask. It might add more logistics like who is going to bring the food/cook the food, who is going to clean everything up.
A private room in a restaurant seems like the easiest (linens, chairs, staff, ambiance are all ready there). Sometimes restaurants can help you create a shortened menu, so that guests can order one of three items, etc.
If everyone is local to your area, then maybe something in the park with a few hors d'eourves would be appropriate. If you have guests that have to fly in and rent cars/hotels, I just feel like they need something "more" for their travels if you know what I mean. But if a park wedding with light snacks is all you want to pay for, then your invitations should convey that type of wedding/reception so that guests can decide.
PS I was in the middle of planning a wedding and my dad was given 4 months to live. The wedding was in 5 months. We ended up cancelling the wedding we had planned, and had a private wedding after he passed away. My sisters were telling me to not have a wedding earlier just so dad could be there because they did not want to fake their happy smiles just for my sake. I know everyone's family is different, but no one was really interested in a wedding when dad was dying. It was OK, I did not want a wedding in my dad's state either. Without wedding $$ on my plate or mind, I was able to fly home often during that time frame to spend time with him including the night he passed away. Best of luck to you guys.