My group and I literally did every quest and side quest in the Rise of the Rune-lords Anniversary ed Chapter/Book one Burnt Offerings. Ameiko became a noble inheriting it legaly in title and land and properties is one of those quests out comes. Our group combed every EXP, treasure and allies we could get our hands on and by the end of Book/Chapter 1 we were about Lv 6 on the slow progression chart with party of 2 PCs and 2 NPCs. Total amount of GP in we meticulously scrounged up was around a little over 50,000 GP. We decided the to take Thisletop as our base of operations from here on as well as giving a sizable donation to the city of Sandpoint. Can this donation get a legal title of nobility if not how can we do it in game?
50,000 gp is a considerable amount of money, but not enough to buy a title of nobility. You can buy lands or a huge manor, but there are few official rules to pull this out.
Even James Jacobs (Paizo's Creative Director) could not give a direct answer about the cost of a farm (land and everything). So I would suggest you start looking at the (optional) rules for Kingdom Building for guidance.
The game has an economy that's based pretty much SOLELY around magic items. As a result, things that are expensive but aren't magic items are always going to be weird; either a house is going to be so expensive that no farmer could ever afford one, or it's going to be so cheap that every PC can buy one at 2nd level, it seems. Which is why, for the most part, the game ignores things like that.
In the Kingmaker adventure path, we solve the problem by basically inventing a new type of currency: the build point. These are what are used to build farms and houses and the like; there's a correlation between build points and gold, but it's not really a 1 to 1 relationship since build points function as a combination of gold, tools, time, talent, and other factors needed to build structures.
For most games, though, if you want to enter the topsy-turvy world of real estate, my suggestion is that houses and farms and structures should be priced realistically, so that, say, a farmer WOULD be able to afford one after many years of work. This means that you could, basically, buy a bunch of farms with a +3 sword, but that's kinda cool too...
While you do not need to use all the rules for building kingdoms, they do give some tips about how to start an area owned by a lord or similar wealth person (these would be your group). You don't need to do the turn-by-turn game of managing a kingdom/fiefdom, and even if you do, I would suggest you guys start small and only play with one hex (a 12 by 12 miles piece of land) at a time, build on it, and heap the rewards.
The land of Varisia is huge, and there are many uncharted areas, wilderness without farms or civilization. The area around Magnimar is full of farms owned by noble families, and Sandpoint is no exception. But even the Kaijitsu got their aristocratic title due to their glasswork trading, so we know it's not impossible to obtain aristocracy through money.
By the end of Tears at Bitter Manor, the player characters are rewarded with the first refusal of a manor (worth about 26,000 gp to buy), as long as they also promise to keep the surrounding wilderness area free of monsters and bandits.
Do note that this includes the land around the manor, as that value is higher than a small castle (7,390 gp) from the (optional) downtime rules.
One of my players in Runelords had a PC cousin to the Deverins so when he went looking to improve the family name it was easier. Now historically, Sandpoint was founded by noble families of Magnimar, most ood whom gained their titles by being the most wealthy, influential folks around. Your PCs may want to try to replicate this by buttering up (or flat out bribing) the corrupt Mayor of Magnimar. They might also try to get the nobles of Sandpoint to put in a good word for them. Hope it helps!