Of course. In fact, Syria and Jordan are among the safest countries in the world for tourists.
In Egypt there are the obvious sights all tourists visit- the Pyramids. However, you will find the Pyramids swarming with other tourists and countless would-be tourguides who, if given the proper chance, will hound you until you give in. During Mark Twain's trip to Egypt, he was so pestered by one guide that he offered him $100 if he would throw himself off of the Pyramid first. Luxor and Karnak (down the Nile in Southern Egypt) will probably be less crowded than the Pyramids. In general, you'll find Egypt hot, crowded, and noisy so you probably won't want to spend more than a week there.
Jordan is far quieter than Egypt, with fewer tourist-traps too. However, asside from Petra (a city carved out of living rock, famous as the sight of the filming of the third Indiana Jones movie) Jordan has little to offer. Three or four days is all that you'll need in Jordan.
Syria is similiar to Jordan in many respects. However, out of all the countries in the Middle East, Syria is probably the best destination for tourists. Syria's long fight against Globalization and Westernization have allowed it to preserve much of its culture. At the same time, Syria is a veritable treasure-chest of history. Damascus (the oldest continuously habited city on earth) contains such ruins as the Roman Temple of Jupiter, the Byzantine Citadel, Ummayed Mosque (the 4th holiest site in Islam), Straight Street (which isn't straight), the tomb of Saladin, and the house of Ananias (now a church). Near Damascus is a village called "Maaloula", famous as the last place on earth that Aramaic (the language of Christ) is still spoken. In addition to this there is the Crak de Chevalliers, the largest and strongest Castle ever built and the best preserved Crusader castle in the Middle East. Aleppo contains the reknowned Aleppo Citadel. Not far from Aleppo is a village called Daer Semaan (Simeon's Village), above which are the ruins of a fortified church reffered to as "St. Simeon's Citadel". Until the construction of the Hagia Sophia in Constantinople, St. Simeon's was the largest church in the world.
I have claimed that these countries are safe, however, there are still rules that tourists should follow.
1. Dress modestly to respect the culture. Long, loose slacks; full length sleeves; and loose shirts are usualy good for both modesty and comfort.
2. If heckeled or annoyed by a guy, simply call for help or make a scene and everyone within a quarter mile radius will come to your aid.
3. Never, under any circumstance, voice support for the state of Israel.
4. Never walk into a mosque with your shoes on or walk behind the altar of an Orthodox church.