I am a fairly new/young private pilot with less than 200 hours total time. I am so tired of flying at low altitudes in the 172. I would really like to take it up to it's service ceiling for a nice view but I do not want to fly a great distance in the climb. Is it legal to do a spiral climb to let's say 12,500 feet MSL? I want to see my neighborhood from a really high view but I am not sure if that would be considered reckless operation. Any answers, suggestions or advise?

If you're VFR and free of Class A/B/C/D, or any other form of controlled airspace... do what you want. Not to sound terse but I would read all of FAR Part 91 and make sure you understand it. Would you call circling VFR in a climb reckless? If it is, I'm done flying.

Make sure you have your transponder on above 10,000 ft. And that you suck O2 anytime you're 12,500-14,000ft for more than 30 min.

You will never get it to that altitude, especially if it is an older one. Just because it says it can, doesn't mean it can or you should. I don't see the point of going this high? Houses look the same regardless of the altitude and honestly you get a better view at 2-3k while keeping it safe.

How about you go get a multi-engine rating or tailwheel to keep yourself entertained for now. You are exhibiting a dangerous attitude that has killed many in the past. Before you go do something stupid, write a letter to your parents, friends and tell them how much you miss them and why you decided to do this. Maybe that will wake you up and show you are not invincible.

Tell that to my 1980 172P, I've taken her to 14,000ft on several occasions. Before that I took a 1976 172M (only 150HP) up to that same altitude.

I fail to see how this is a dangerous attitude if proper precautions are taken....

Watch out for the effects of hypoxia. Your body reacts to density altitude not true altitude.

Yes. Unless you know how your body handles it, better take some O2 above 10k.

Also you should have no trouble getting any 172 to service ceiling with one pilot and less than full tanks.

Skydiver pilots do this all day long and they do not use spirals because turning uses up more energy than straight-line climbing. What you should do is look at your sectional and choose a point about 10 miles away, fly there and then come back to the origin climbing the whole time. Lean out your engine as you go so you get max power. On the descent don't forget to use the carb heat, and descend a few miles away from any airport pattern.

...and be careful to not shock cool the engine.

I took a 1966 C-150 with a pull starter up to 14,100 feet some 30 years ago.