Before I say anything realize that everything you read here including my post comes from anonymous internet posters that know nothing about you, your situation, or what is best for you. Therefore take everything you read with a major grain of salt including my post below.
First off congratulations on getting through the LSAT with your numbers you can get into a number of ABA schools.
LSAT RETAKE QUESTION:
A 162 is a solid score and the reality is many people do worse in the pressure of the real scenario and if you end up enrolling in law school it will be the first of many times where you don't do as well as you expect. On the first day of school everyone is pretty convinced their LSAT score was a fluke and they will certainly be in the top 10% of the class. 100% of students sincerely believe this, but you don't need to get past first grade math to see how that works out and then 90% of students end up worse than they thought. Do you not be disappointed by your score it is quite good and not doing as well as you expect is something all law students needs to get used to.
As to whether or not to retake I would encourage you to apply to schools as planned. If you put off law school until the next cycle odds are life will get in the way. You will start a job, get married, have a kid, or simply think you will do better on the next LSAT. So apply as planned and then schedule yourself for the February LSAT if your score improves dramatically then weigh your options. If it comes back about the same then you got the ball rolling. Then as I understand almost all schools have gotten rid of the averaging of LSAT scores, but I could be wrong check with individual schools on that. If that is the case you are in an everything to gain and nothing to lose scenario. If you pull a 172 in February then it may be worth waiting to apply, but odds are you won't and then your apps will already be sent out and everything will go as planned.
-RANGE OF SCHOOLS-
There is no range of schools you should consider find what school suits you best. Consider the location, cost, and how you feel about the school. Do not let U.S. News or anonymous internet posters tell you what range of schools you should go to. At every law school across the country you will learn the same exact thing. Your first year will be torts, property, criminal law, criminal procedure, contracts, Con-Law, LRW, or some variation on that.
When you choose your school think about where you are going to live, your personal life family, friends, and the costs you are accruing. Law school does not exist in a vacuum and you will have time to be a human being during law school. I don't know if this is your situation or not, but so many students will go to school across country because U.S. News said X school was 84th while Y school was 93rd and truth be told it doesn't make much of a difference. It certainly isn't worth altering your life for the location of your school will play a bigger factor than almost anything else.
Furthermore, each school has a culture to it. Make sure it suits your style when I was choosing schools there were a few that I really liked and others just felt off to me. However, that was my own personal feeling and what I liked you may have hated and vice versa.
With your number you will have the opportunity to get numerous scholarships at a variety of schools. Getting an ABA degree debt free is something to consider particular if it is located in the location you want to practice in.
My main point is there is no range of schools you should be considering. See what suits YOUR personal needs with location, cost, and culture. No magazine or anonymous internet poster can possibly know what is better for you than yourself. Remember wherever you go is a 3 year commitment of your life, 100,000 or more of YOUR money, and YOUR legal career. So listen to your gut and realize a lot of things you read on the internet or in opinion magazines should not be taken that seriously.
However, I could be 100% wrong in everything I have said, but I do think it is important to remember this is YOUR life and nobody knows what is better for you than yourself.
Hopefully some of this is helpful and congrats on the LSAT and good luck in your future endeavors.