I looked at the Swan and saw rates as low as $212 per night for some nights in April. You need to add about $25 resort fee and $17 parking fee to that, though. I didn't check the Dolphin, but that is also a possibility for a deluxe hotel walking distance to Epcot and DHS, and possibly in your price range.
There are a lot of different discounts available at the Swan/Dolphin - teacher, nurse and military are usually the best. CAA will also get good discounts. Check to see what the different ones are that you might qualify for when you call or look online. SPG membership can score you a room category upgrade, if available. You do need to ask. My DIL has asked and received an upgrade on every visit at the Dolphin.
The Swan has two queen beds and the Dolphin has two doubles.
Fresh at the Dolphin serves good smoothies and lots of fresh breakfast items. we have found the breakfast to be quite good there. Wherever you eat in WDW, they will take good care of your son's allergies. My Mom has several allergies and we have always been looked after very well. Be sure to let them know when you check in, they will likely have the chef come to let you know what is safe or not for your son to eat. Advance notice will sometimes allow them to prepare something special for him. (My DGD also has shellfish and egg allergies and has had excellent assistance getting lots of good food that is safe for her in WDW. Last visit in Nov the Chef made her a special dessert that looked absolutely awesome! It was so sweet of him! Looking after specific health issues is still one area where WDW CM's shine, IMO.
Back to the resort:
If you want real WDW, as others have said, standard view at the Animal Kingdom Lodge or a room at any of the moderates would likely fit your budget. The moderate that I would choose would be CSR or POR with 9 year olds. A preferred room is worth the extra $$ as it will keep you in the most convenient area of the resort. If you book Business class at CSR, you will have fruit, cold cereal, pastries, yogurt, coffee, tea and juices available in the lounge for breakfast. Depending upon what your son's allergies are, this may or may not work for you. There is an additional cost for BC, so a preferred room might be a better option, in your situation.
Keep checking for discounts. Availability changes all the time. You can usually get a discount applied - as long as there is availability for your room type and resort.
Good luck! I hope that you have an awesome trip!