Hi, for a shorter ride you can go around the surrounding neighbourhood to the east. Many of the roads have onroad bike lanes. You can cross the bridge on Upper Middle to get to another neighbourhood.
You can go south to get to the lakeshore, which has the waterfront trail. In Oakville and Burlington it is more on road than trail. Hamilton beach has a great trail (20 min car drive), but can be crowded on warm weekends. Hutch's for fish or hamburgers is very popular.
To the north there are a lot of quieter country roads, with some good climbs if you are looking for such. I live more to the east so not sure of the best route north. Do not ride on Bronte. You could drive 5 minutes to a parking lot for the 407 highway.
Try mapmyride or ridewithgps for some routes. If you want more specifics I will check back to see your questions.