Lawrence is a tough market for nurses looking for employment. There are FIVE (KU, Washburn, Neosho, JCCC, and Baker University) nursing schools
within a 50 mile radius so there are no shortages here! You can try getting on with a particular physician in town (don't expect to be paid well, though) or go through Stormont Vail in Topeka (see their web site) and get a job with the Cotton O'Neal Clinic in Lawrence (Stormont owns Cotton O'Neal). Lawrence Memorial Hospital is ok, too, but it's very difficult to get on there. You really have to know someone to even get an interview. Douglas County Visiting Nurses is an option, too. They have some wonderful staff there; Southern Care is another hospice in Lawrence that is a good place to work.
Topeka has a lot of opportunities and is only about 30 miles west of Lawrence. You can check out St. Francis Hospital and Stormont Vail Healthcare to see what opportunities appeal to you. They both have very user friendly web sites and I've worked at both hospitals over the years. Stormont is working towards Magnet status and is a wonderful place to work overall. Very supportive of their nursing staff, good benefits and the pay is comparable to KC hospitals. St. Francis is in the process of building a new hospital on the West side of Topeka so they are going through a transition phase right now.
Hope that helps! Good luck!