Section 8 and Eden vouchers accepted!!! Grasmere Apartments offer affordable 1 & 2 bedroom units located in the 44112 area of Cleveland, minutes away from University Circle. Our spacious apartment homes offer new appliances, walk-in closets, and upgraded kitchen and bathrooms. Income-based rent program. Rates range from $785 – $1,005 per month based on verified household income and objective qualification criteria, applied consistently to all applicants.