<PAGE>

                                                                    EXHIBIT 10.4

                      AMENDMENT TO MANAGEMENT AGREEEMENT


     This First Amendment to Management Agreement ("Amendment") is made and
entered into as of May 10, 2001, by and between APPLE SUITES MANAGEMENT, INC., a
Virginia corporation ("Owner"), whose address is 306 East Main Street, Richmond,
Virginia, 23219 and PROMUS HOTELS, INC., a Delaware corporation ("Manager"),
whose address is 755 Crossover Lane, Memphis, Tennessee 38177.

                                  WITNESSETH:

     WHEREAS, Owner and Manager have entered into that certain Management
Agreement dated April 26, 2001 ("Management Agreement") for that certain
property known as the Homewood Suites-Atlanta Buckhead and more particularly
described in the Homewood Suites License Agreement attached as Exhibit "A" to
the Management Agreement;

     WHEREAS, Owner and Manager desire to amend the Management Agreement on the
terms and conditions set forth herein;

     WHEREAS, the Management Agreement, as amended hereby, shall continue in
full force and effect;

     NOW, THEREFORE, in consideration of the mutual covenants herein contained
and other good and valuable consideration, receipt of which is hereby
acknowledged by the parties hereto, Owner and Manager hereby agree as follows:

     1.   Amendment.  This Amendment modifies and amends the Management
          ---------
          Agreement. In the event of any conflict between any provision of this
          Amendment and any provision of the Management Agreement, this
          Amendment shall control. The Management Agreement, as hereby modified
          and amended, shall be referred to herein as the "Agreement." Any
          reference in the Management Agreement to the "Agreement" shall, from
          and after the date hereof, be deemed to refer to the Management
          Agreement as hereby modified and amended.

     2.   Term.  The Term (as defined in the Management Agreement) set forth in
          ----
          Exhibit "B" to the Management Agreement is hereby deleted in its
          entirety and replaced with the following: "Five (5) years from the
          Effective Date." The Agreement shall terminate on April 26, 2006,
          unless earlier terminated in accordance with the Agreement.

     3.   Manager's Termination Rights.  All references to "Sale Termination
          ----------------------------
          Fee" in Sections 9.02 and 9.05 of the Management Agreement are hereby
          deleted and replaced with "Early Termination Fee."
<PAGE>

     4.   Owner's Termination Rights.  Section 9.04(a) of the Management
          --------------------------
          Agreement is hereby deleted in its entirety and replaced with the
          following:

               Provided Owner is not in default under this Agreement at the time
               of delivery of the Termination Notice (as defined herein) or on
               the Termination Date (as defined herein), Owner shall have the
               right, after the first anniversary of the Effective Date, to
               terminate this Agreement by giving written notice (a "Termination
               Notice") to Manager setting forth an effective termination date
               which shall be the last day of a month (the "Termination Date")
               and which shall be not less than six (6) months nor more than
               twelve (12) months after the date of such Termination Notice and
               shall in no event be prior to the first anniversary of the
               Effective Date. If Owner terminates this Agreement pursuant to
               this Section 9.04(a), in addition to payment of all other fees
               and reimbursable sums due to Manager on the Termination Date,
               Manager shall have the right to receive the Early Termination Fee
               calculated in the manner set forth on Exhibit "B." Such
               termination shall be effective so long as on or before the
               Termination Date Owner pays to Manager the Early Termination Fee
               and all amounts determined by Owner and Manager, each acting
               reasonably and in good faith, to be due and owing to Manager
               pursuant to the terms and provisions of this Agreement.

     5.   Early Termination Fee.  The paragraphs entitled "Sale Termination
          ---------------------
          Fee" and "Cancellation Termination Fee" in Exhibit "B" are hereby
          deleted in their entirety and replaced with the following:

               Early Termination Fee.  The "Early Termination Fee" shall be as
               ---------------------
               follows: (i) $350,000 if the termination of this Agreement occurs
               pursuant to Sections 9.02 or 9.05 of this Agreement before the
               first anniversary of the Effective Date, (ii) $350,000 if the
               termination of this Agreement occurs during the period commencing
               on the first anniversary of the Effective Date and ending on the
               second anniversary of the Effective Date; (iii) $250,000 if the
               termination of this Agreement occurs after the second anniversary
               of the Effective Date but on or before the third anniversary of
               the Effective Date; (iv) $100,000 if the termination of this
               Agreement occurs after the third anniversary of the Effective
               Date but on or before the fourth anniversary of the Effective
               Date; and (v) $25,000 if the termination of this Agreement occurs
               after the fourth anniversary of the Effective Date.

     6.   Miscellaneous.
          -------------

               6.1  Counterparts.  This Amendment may be executed in
                    ------------
                    counterparts, each of which, when executed and delivered,
                    shall constitute an original, and all of which together
                    shall constitute one and the same agreement.

               6.2  Applicable Law.  This Amendment shall be construed under
                    --------------
                    the laws of the State of Georgia.
<PAGE>

     IN WITNESS WHEREOF, Owner and Manager have caused this Amendment to be
executed the day and year first above written.


                              OWNER:

/s/ Gus G. Remppies           APPLE SUITES MANAGEMENT,
-------------------
Witness:                      INC., a Virginia corporation


                              By:  /s/ Glade M. Knight
                                   -------------------
                              Name:  Glade M. Knight
                              Title:  President



                              MANAGER:

/s/ Dawn Badowski             PROMUS HOTELS, INC., a Delaware
-----------------
Witness:                      corporation



                              By:  /s/ Rick Schultz
                                   ----------------
                              Name:  Rick Schultz
                              Title:  Senior Vice President