Visiting المدينة is highly مستحب — pray at Masjid al-Nabawi, visit the Rawdah, Masjid Quba, and Uhud; the Haramain train connects مكة to المدينة in 2-3 hours.
Visiting المدينة is highly مستحب and most الحج packages include it, though it is not a ritual obligation of الحج. النبي (صلى الله عليه وسلم) said: 'A الصلاة in my مسجد is better than a thousand الصلوات in any other مسجد except المسجد الحرام' (Bukhari and Muslim). There is no الإحرام requirement for visiting المدينة — you travel in your regular clothing.
Key sites to visit include: Masjid al-Nabawi for الصلوات and visiting the Rawdah (the area between النبي's pulpit and his chamber, described as a garden of Paradise), sending salutations upon النبي at his grave, praying at Masjid Quba (praying two ركعة there equals the reward of an العمرة عند hadith), visiting the Uhud battlefield and the martyrs' cemetery, and exploring the famous date market. The Haramain high-speed train connects مكة to المدينة in about 2-3 hours and is the most comfortable option. Most الحجاج spend 3-5 days in المدينة.
Source: صحيح البخاري; صحيح مسلم; سنن النسائي