The best and most memorable gift to give a father on Father's Day is the gift of bonding -- the ultimate present of creating memories to look back on. Planning various outings with your father, grandfather, uncle or other man in your life you highly regard as a father-figure doesn't have to cost much or anything at all. The most important part is taking advantage of the alone or quiet time to open up to each other in conversation.
If you and your father are the outdoors type, you can try camping at a new destination or going back to a treasured spot that he enjoys most. Take advantage of the fresh air and go fishing, check out a new nature trail or build a camp-fire. Most importantly, embrace the quiet and solitude of being together - keep your phone hidden and turn your ringer off.
Cooking or grilling is also a great activity to do together. Check the web (specifically Pinterest) for new grilling ideas. This is a great option not only for you two to do together, but also for the entire family to enjoy.
Sporting events are a great time to get out together, especially if this isn't something you do together regularly. You can head to the event extra early to check to grab a bite to eat and drink and walk around - perfect time for conversation if it's not noisy.
Depending on where you live, take an all-day (or few hour) road trip and explore new places. If not by car, public transportation would be another great option to consider. A long train or bus ride will give you both quality time to sit and enjoy each other's company and check out a new or familiar place you don't visit often - or at all.
Lastly, whatever you decide, make sure to bring your phone or camera to document moments on the special day. Photos and videos also make a great present after the day is over - your father (and you) can look back and remember the memories of that special day for a long time.