Three days in Nara
Nara is one of the jewels of Japan. However, most visitors only have a day - or an afternoon - for the city, which is enough time to hurry through Nara Park, but leaves out some other worthy sights and experiences in the area. If you have the luxury of a few extra days, you'll find a lot more to discover.
Make hotel reservations before you arrive, especially if you have a specific hotel in mind. While Nara is well-served by hotels, it is a favorite destination for tour groups, so accommodations can book out quickly and suddenly - particularly for cherry blossom season in April, but also in mid-January for the Mount Wakakusa Fire Festival and early-to-mid August for Nara Tōka-e, the light festival.
If you're staying in the Naramachi area, then start your first day with a leisurely wander around the streets of the old merchant area, poking your head into any small museums that catch your eye. (Alternatively, you can save Naramachi for the late afternoon and include a stop at Harushika (春鹿), a Nihon-shu (sake) brewery, as reward for a day well-spent.)
The main sights in Nara Park, especially Tōdai-ji, are going to be crowded at any time of the day. There's no sense in rushing to get there at dawn to have it to yourself; the deer have the place staked out around the clock. Instead, make your way over to Nara Park at your own pace. Try to begin or end your day at Tōdai-ji for a look at the spectacular Daibutsu-den and the Daibutsu (大仏). Don't plot out a strict time-managed course, though. The atmosphere of Nara Park is a true marvel, especially if you've spent the last several days shuttling around on the train. Don't search; discover.
At the edges of the park, you'll find Kōfuku-ji (興福寺) and its five-story pagoda, the terrific view from Sarusawa-no-ike Pond, and the Nara National Museum. Save the museum for later, though, and head into the nearest section of the Kasuga-yama Hill Primeval Forest (春日山原生林). You're bound to come across Kasuga Taisha (春日大社) and its famous stone lanterns somewhere in the midst of it. Take your time, and see where the path takes you. On the other edge of the forest, you may come across Shin Yakushi-ji and its warrior guardian statues.
In the morning, pursue an interest: Isui-en (依水園) is at the edge of Nara Park if you're keen on Japanese gardens, or check out the relics at the Nara National Museum or Tōdai-ji's Shōsō-in (正倉院). If it's Saturday (in April-July and Sep-Nov), you can join a morning walking tour of Naramachi (10:00-13:00) with a local guide, leaving from the Tourist Information Center on the ground floor of Kintetsu Nara Station. Reservation is not required. Just show up by 9:55. The tour fee is 2000 yen per person and 1500 yen for students. Children under 15 go free. 
In the afternoon, take a bus to visit some of the sights west of the city:
The following two sites are relatively close to each other.
The ride on bus to the two temples above will pass by the Palace Site, allowing you a glance over Suzaku Gate.
Horyuji is one of the oldest and grandest Buddhist temples in Japan, and it's only a short trip from Nara - three stops from JR Nara station on the Yamatoji line. Much better known to Japanese tourists than to Westerners, the vast grounds of the Western Temple (西院 Sai-in) and the Eastern Temple (東院 Tō-in) can easily fill a full morning, with nary a reminder of modern hustle and bustle along the way (save for lines on busy days). When you're done, leave through the main gate and stop for lunch at one of the restaurants near the approach to the temple.
If your next destination is Osaka, take the Yamatoji line a mere 23 minutes to Tennōji. However, if you're making your next connection through Kyoto, head back to JR Nara station to change lines, and you can devote an afternoon to Uji on the way back to Kyoto. Raise your ¥10 coins in tribute to Byōdō-in (平等院), enjoy a walk by the Uji River and don't miss the most renowned tea in Japan.
By now, after three days of temples and the atmosphere of the ancient capital, you should be ready for the concrete, neon and wires of modern Japan.
If you're there in early April and you're up for some cherry blossom chaos, don't miss Yoshino (吉野), which has been cited for centuries as one of Japan's most beautiful sakura viewing spots. And if Naramachi struck your fancy, try Kashihara (橿原), the site of Japan's pre-Nara capital, Fujiwarakyo (藤原京), which incorporates Imai (今井町), full of old merchant houses dating back from Edo period. On the ancient capital circuit, Asuka (飛鳥) is also within easy reach.
The deer in Nara Park tend to be friendly and perhaps overly eager to eat shika-senbei (¥150) biscuits from the hands of tourists. Small children may be frightened to have the suddenly manic deer coming after them, so it may be best to feed the deer yourself and let the kids watch. Steer clear of any deer which still have their antlers. They can be aggressive and their antlers can injure you.
If you are allergic to pollen, beware: the heaviest cedar pollen fluctuation in this area is usually from mid-February to April.