Well as my dad always said. If you don’t know what the problem is always start with the cheapest thing and go from there. If you want to check your tires try switching the fronts for the back, see if the problem is still there. Then look at your stabilizer shock,take it off, and see if it is blown. (if the piston has resistance then it probably won’t be the problem). The Check the front shocks and check to see if they have resistance. These are 3 of the common problems for the Wobble and can be easily (depending on the rust situation on the bolts) checked at home for free.
Also you can check for looseness in your front end yourself. Jack up one of the tires; grab the top and the bottom of the tire and shake, then try side to side, there should be no play... Then with the help of a friend lower the front tire down about 1-2 inch off the ground, slide a 2 to 3 foot steal bar under the tire. While you are looking under the front of the Jeep have your friend lift up and down on the bar. Look for any movement in the linkages or ball joints; again there should be none. Then check the other side the same way. Just make sure when the Jeep is up that the jack isn’t on any of the suspension parts.
Always start easy..