Company Names, addresses, dates:
  S.P. Hite & Company, 320-322 Loudon Ave NW, Roanoke VA (1905-1910) ^1,2
  S.P. Hite & Company, 323 Center (2nd) Ave NW, Roanoke VA (1912-1920) ¹
  S.P. Hite & Company, 320 Loudon Ave NW, Roanoke VA (1922-c.1960) ^1,3

Notes:
S.P. Hite & Company is listed as a "Manufacturing Druggist" in the Roanoke City directories. Note that not every year's city directory was checked, so the dates listed above are approximate.

Dr. Samuel P. Hite (1843-1917)⁴ had a successful business manufacturing drugs in Staunton VA, and in 1905 he expanded by moving to a larger facility in Roanoke, VA. ².
Dr. Hite passed away in 1917, but the company kept going until at least 1960 - that is the year of the last newspaper article/ad I could find that mentioned the company³.


Bottles:

This is a clear 5.75" bottle with a label and embossing. It says: label: HITE'S / (picture of man) / PAIN REMEDY / ALCOHOL (65%) / ESSENTIAL OILS, ETC. / ... S.P. HITE Co., Inc. / Roanoke, Va. vertical embossing: HITE'S PAIN REMEDY / FOR MAN AND ANIMALS / ROANOKE, VA.

This is a clear 4.5" machine-made screw-top bottle with a label that says: label: Hite's / FAMOUS REMEDY / ... / PREPARED BY / S.P. HITE Co., Inc. / ROANOKE, VIRGINIA 24003 / Since 1871 / 2 FLUID OUNCES The bottle came in the cardboard box shown, which says: box (front): Original / (picture of man) / Hite's / FAMOUS REMEDY / ... / S.P. HITE Co., Inc. / ROANOKE, VIRGINIA 24003 box (side): HITE'S FAMOUS REMEDY / Prepaired by the same formula since 1871

This is a letter with a printed letterhead that says: top left: (picture of Hites Pain Remedy bottle) top right: (picture of Hites Vanilla Extract bottle) top Center: S.P. HITE COMPANY, INC., / MANUFACTURERS OF / "HITE'S PAIN REMEDY" / HIGH GRADE FLAVORING EXTRACTS, / STAPLE, / PROPRIETARY AND TOILET ARTICLES / GUARANTE NO. 2384. Letter Content: Roanoke, VA., Sept. 30, 1911, ...