If you are in to your gardens / horticulture the area around the cottage is very well served with some glorious gardens and houses to visit. Great Dixter is one and very close by. Equally if you are like me and have a weakness for a cup of tea and slice of cake or scone, then you could try the café / restaurant at Blackbrooks Garden Centre on A21, Sedlescombe, Battle TN33 0RJ, if has a surprisingly good selection of food. If retail therapy is your bag then you get this too. So if you are peckish for plants, food on way to / from cottage could be a place to stop off.
Great Dixter also has a small cafe, you can always pop into the cafe without visiting the main house and gardens. It is around the back of the main house, you could then visit the house nursery to pick up a green reminder of your visit.