Here is a guide to plan your tourism into Lake City of Rajasthan. Udaipur offers both luxury and relaxation being oasis amidst desert state. It's cool and green, offers great shopping destination, and has good flavour of royalty, culture, and religion. You should be able to spend 3-4 days easily in Udaipur. Here are some of the key attractions within city.
City Palace was main palace of Udaipur ruling dynasty. Price is little on higher side (Rs. 500 for Indians) but worth there 2-4 hour experience. There are narrow passages and staircases just so you know. View from outside is amazing though from inside is okay.
This historic and revered temple is near City Palace entrance, and you can spend 30 minute here marveling at the architecture.
Fateh Sagar Lake
Fateh Sagar Lake is place where you'd want to spend your evenings. You will find many locals here, enjoying the sunset, breeze or just munchies. You can take horse and camel rides as well.
Bharatiya Lok Kala Mandal and/or Bagore Ki Haveli
Both of these locations offer you culture dance show in evenings. You must make it to at least one. Tickets are available at venue, though you should reach 30-60 minutes in advance to secure limited seating. Timings vary but is around 6 pm for both. Apart from culture show, there is small accompanying museum as well.
Lake Pichola view from Ambrai ghat or Gangaur ghat is smaller version of Fateh Sagar Lake. It's fairly crowded area to sit and enjoy the breeze. One may also take boat ride around Jagmandir Island.
This is monsoon palace for royalty. There is not much palace-wise but it's on hill so you get decent view. Last kilometer is bit uphill so you may drive your car or hire a shared jeep.
Sajjangarh Wildlife Sanctuary
This is fairly standard zoo, and you can visit this if you are going to Monsoon Palace as it's just at the entrance to that.
Sahelion Ki Bari
It was private garden for royal ladies. Now it's just simple park.
Nearby Udaipur (within 40km)
Temple of baby Krishna is very popular and expect crowd all the times. Temple opens at specific times throughout the day (every few hours, for few minutes) so be ready for long queues. Market around is nice for ad-hoc shopping and eating.
Ekling Ji Shiva Temple
The Eklingji Temple, one of the popular pilgrimages of Rajasthan is located at a distance of 22 km away from Udaipur. It's very old dilapidated temple but that offers its own charm.
Sahastra Bahu Temple
Temple of Vishnu, locally sometimes call Saas-Bahu temple, is around 20 km from Udaipur. It's great architectural splendor though partly in ruin now.