Dress appropriate to the seasons.
It gets veeery cold in winter - woollen coat/duck-down jacket, hat, gloves, scarf.
It gets veeery hot in summer - singlets/tee-shirts, shorts/skirts/cargos/jeans.
It's medium (cardigan and light jersey/coat weather) in autumn (Sept, October, November) and spring (March/April/May).
Camping/Beach/Outdoor Gear: Nara Park is great for picnics. It's picturesque and interesting to watch Japanese families, or relax with a book by the pond. So, when you get there, pack a picnic! Buy some ume-shu (Japanese plum wine) and buy a bento (Japanese packed lunch) and have a great Japanesey day!
Miscellaneous: And if it's summer when you have a picnic. You may need to bring mosquito repellent. They are vicious, hungry little insects!
Luggage and bags:
If you plan on doing a lot of train travel when you are in Japan then I suggest that you decline from bringing large, heavy suitcases. Most train stations in Japan have huge staircases (often no lift) so lugging a big suitcase is not an easy task. I suggest a good backpack would be a good choice.
Clothing/Shoes/Weather Gear: Rainy Season is around June/July and rain weather gear is essential. I just use an umbrella but there have been times that I have got completely soaked!! I can't buy shoes in Japan so I have had to think carefully before I came about what kind of footwear to buy. Note: Easy to slip on and off shoes are best and if you are going to work in a public building you will need 'indoor' shoes to wear. The Japanese always take their outdoor shoes off before entering their house or work.
Toiletries and Medical Supplies: Most things you will need can be purcahsed here. I don't recommend going to a hospital in Japan unless you really need to. In most cases the pharmacist will be able to help you if you tell them what is wrong and what kind of medicine you are looking for (a phrase book will have this in it).
Camping/Beach/Outdoor Gear: Nara Prefecture and nearby Wakayama Prefecture are great places for camping in. It is a little hard to find good camping spots in Japan as it is not a common pastime for the Japanese but if you would like to go camping then bring along your tent and sleeping bag and have a go!