Country around Melbourne
 

Our travel agent has us spending 4 nights in Melbourne in August. We will already have been one week in Sydney. I was kind of hoping to stay out of the city and drive into Melbourne.
Are there any country towns around Melbourne we could stay at that are scenic, interesting, quiet, and would serve as a base to explore the surrounding countryside?

You could try the Mornington Peninsula:
http://www.visitmorningtonpeninsula.org/

Sorrento on the Mornigton Peninsular is about an hour from the CBD. From there you can visit Phillip Island or take the car ferry across to Queenscliff and The Great Ocean Road. In the other direction Daylesford has many B&B's and other accommodation. It is in the Goldfields area and about 75 mins. from the CBD. From Daylesford you can visit Ballarat, Bendigo, Castlemaine etc.
In yet another direction, Healsville and the Yarra Valley wine growing area is a good option. Lots of places to stay, gourmet food shops and really a lovely area. About 60 mins. from the CBD. Hope that is been of some help, but bear in mind that Melbourne is a different city from Sydney and it is easy to go for day trips into the country from the CBD.

Another place worth considering is Olinda in the Dandenong Ranges about 50 mins. from the city. There are heaps of B&B's in the Dandenongs and it is a beautiful area. I can recommend Folly Farm at www.follyfarm.com.au

I checked out the Mornington peninsula and it looks like a great place to stay and explore from. Our travel agent suggested either the Sebel Heritage Yarra Valley (I don't know where that is in relation to Mornington) or the Peppers Moonah Links Resort in Fingal. We probably won't be playing any golf so I'm not sure why she recommended them.
We will have a car and hope to rent some bikes and get into the small roads.

The Mornington Peninsular is a wonderful area close to the city, excellent beaches, vineyards and ideal for what you have planned. I know both properties you mention, they are upmarket and really golf course resorts. The Sebel Heritage boasts a Jack Nicklaus designed Golf Course and the Peppers at Moonah Links is the home of the Australian Golf Union and has hosted the Australian Open. So unless you are a golfer they are a bit of a waste, however the accomodation at both is excellent. The former is about 45 mins. from the Peninsular in the wine growing Yarra Valley while Peppers is right on the Penisular.
Look there is tons of accomodation on the Penisular and I would urge you to ask your travel agent to do a bit more research. www.visitmornigtonpenisular.org is a particularly good site, go to their accomodation and you will see heaps. Lindenerry at Red Hill is an excellent place for instance. Portsea, Sorrento, Hastings, Mt.Martha and Mornigton are all great places to stay. You would enjoy your visit.

Have a look at www.arthursviews.com.au one of the best positions on the peninsular.