I put the following steps together in order of the recommended moves to get 100% favor in all houses. Note, Piscarilius is the slowest and least valuable house to gain favor (IMO), it is recommended to use the Client of Kourend favor scroll to boost Piscarilius from the start due to its slow nature.
Step 1) Complete Client of Kourend - This quest is a baseline to several others in Kourend and will prove useful to get squared aware first. Completion awards a scroll giving 20% favor to any house -- I recommend applying to Piscarilius
**Note -- if you don't apply the favor to Piscarilius you will have to repair cranes at the docks until you have at least 20% favor to complete the Queen of Thieves. Crane repair involves lots of nails and planks. It is also very slow as it awards only 0.5% favor per crane and each crane repair can take a couple minutes if doing it alone. You need at least 30 crafting for crane repair.
Step 2) Complete the Queen of Thieves - This will add another 10% to Piscarilius favor and grant you the first page to put in Kharedst's memoirs. It also grants access to the warrens (shops in the sewers below Piscarilius.
Step 3) Hunt Sandworms - Hunting Sandworms for Tynan (located in the Northeast section of Piscarilus) will take you from 30% favor to 100% fairly quickly. Tynan sells buckets used to collect the sandworms, you'll need a spade! Don't remove sandworms from the bucket, instead click "use" and use on Tynan to give him the buckets of worms for favor. Keep brining Tynan sandworms until you have 100% favor.
Step 4) Push Plows in Hosidius - Plowing the fields will earn you enough favor to get to 5% -- bring a hammer to fix broken plows
Step 5) Harvest Saltpetre - Once you have 5% favor you can head to the west of the fields, crossing a bridge until you come to several piles of salt petre scattered around a central structure with an NPC called the Clerk. Dig up salt petre and bank at the deposit box next to the Clerk until you have 850 units. Then head to the town square in Hosidius and purchase enough compost to combine with the salt petre. After combining all the compost and salt petre go back and talk to the clerk, she will take units out of your bank too and award favor so no need to make laps. Now you have enough favor to complete the Hosi quest Depths of Despair
Step 6) Complete Depths of Despair - Go speak with Lord Kandur Hosidius in his house (northwest of the Vineyards). You'll need 18 agility for this quest. After completing the quest you'll have 10% favor to award and should now be at 100% Hosidius Favor.
Step 7) Heal Shayzien Soldiers - Go to the infirmary in Shayzien and heal wounded soldiers using med packs (there is a stock tent just outside the infirmary tent where you can grab med packs). Each pack provides 0.1% favor, do this until you have 5% favor.
Step 8) Kill Lizardmen - I recommend this step as its quicker than medpacking to higher favor levels and gives you the chance to score Xeric's Talisman (a useful teleportation necklace to various locations around Kourend). The talisman comes uncharged and can be charged by using Lizardman Fangs on the talisman. You'll want food and antipoison potions when fighting lizardmen.
Step 9) Complete Tale of the Righteous - Speak with Phileas Rimor in his tent near the bank (north end of Shayzien) to begin the quest.
Step 10) Fight Shayzien Soldiers - Some people recommend fighting organized crime, this is somewhat time consuming so I think fighting soldiers (Tier 1 - 5) in the center circle in camp is the quicker and better way to go. Scoring tier 5 armor is useful if you plan to fight Lizardman Shamans later on as it offers unique protection against their splash attacks. You can repeat fights at different tiers until you qualify for the next tier, I repeated these fights until I had 100% favor.
Step 11) Help Find Books in Arceuus Library - Find books for Sam, Professor Gracklebone or Villia. In return for the books they will give you magic/runecraft XP boosting books. Read them and decide whether you'd like to apply towards magic XP or runecraft. There is also an NPC named Horphis who is seeking dark manuscripts. In addition to returning books, successfully finding a manuscript for Horphis will yield additional opportunities to boost magic or runecrafting XP. Books grant 2.5% favor and Dark Manuscripts grant 5% favor. Note - using Runelite client makes finding the books much easier! I recommend grabbing as many as you can in one go to better your chances of turning in multiple books at once.
Step 12) Complete The Ascent of Arceuus - This quest can be started near Regath's Wares to the Southeast of Arceuss Library. Speak with Mori to begin.
Step 13) Mine Sulphur in Lovekengj - Mining sulphur provides 0.1% favor. Toxic clouds deal out damage very quickly -- a facemask/gas mask/slayer helmet will reduce damage. Note the clouds only deal damage from certain positions, standing on the south end of the pile is the best position to avoid getting hit frequently. Some players also use the nearby spider to provide cover on the southern-most pile. By positioning the spider to the west of a player it is possible to avoid damage from passing clouds. Mine sulphur until you have 65% favor
Step 14) Complete Forsaken Tower - Speak with Lady Lovakengj in the Assembly Chambers (just west of the south bank in Lovakengj) this quest grants 10% favor
Step 15) Deliver Mine Cart Instructions to Operators - Speak to Miriam, the mine cart operator in Lovakengj (just outside the southern bank) to receive instructions. Carry the intructions to the various operators throughout Kourend to go from 75% to 100% favor.
After gaining 100% favor in all houses you can speak to each house architect to complete the Architectural Alliance miniquest.
Hope this helps, good luck!