It's likely Twain traveled to Indianapolis from Paris, IL on January 1, 1872 as he attended church in Paris December 31, 1871. 

Both the New York Central and the Pennsylvania Railroads had connections between Paris and Indianapolis.  The NYC, as per the Wikipedia article, maps the Terre Haute Railroad and the St Louis and Indianapolis Railroads.  The Wikipedia article for the Pennsylvania Railroad maps the Paris and Terre Haute Railroad and the Terre Haute and Richmond Railroad. This line was associated with the Vandalia Railroad.

January – Sam’s article “A Nabob’s Visit to New York” ran in American Publishing Co.’s in-house promotional monthly, American Publisher [Camfield, bibliog.]. See Roughing It, Ch. 46.

January 1 Monday – Sam arrived in the evening to lecture in Association Hall, Indianapolis, Indiana – “Roughing It in Nevada” [Schmidt].

Sam was billed $21 by Hartford Drs. Taft & Starr for “professional services from July 1, 1871 to Jan 1 1872” [MTP].

January 2 Tuesday – Sam lectured in Opera House, Logansport, Indiana – “Roughing It.” Before the lecture he wrote from Logansport to James Redpath.

“Had a splendid time with a splendid audience in Indianapolis last night—a perfectly jammed house….I like the new lecture but I hate the ‘Artemus Ward’ talk & won’t talk it any more. No man ever approved that choice of subject in my hearing, I think” [MTL 5: 1].

January 3 Wednesday – Sam lectured in Richmond, Indiana – “Roughing It.” He also wrote his mother, Jane Clemens:

Dear Mother—Enclosed find checks for three hundred dollars. Please drop Livy a line acknowledging receipt of them, & tell her to let me know right away.

January 4 Thursday – Sam arrived in Dayton, Ohio and stayed at the Beckel House, Room 169. In the evening he lectured “Roughing It” to a full house in the Music Hall. He wrote John Henry Riley about plans for the diamond book, thinking that he’d be ready to start the collaboration around the first week in March [MTL 5: 2-3].

Friend Riley—

Heaven prosper the Minister to S. A! Amen.

January 5 Friday – Sam lectured in Opera House, Columbus, Ohio – “Roughing It” [MTPO].

A receipt from John Hooker for $100 for “house rent in full” is likely for one month, since later receipts for Hooker’s Nook Farm rent were $300 per quarter. Bill paid to E. Habenstein, baker for Livy, products not legible [MTP].

January 6 Saturday – Sam “hired a locomotive…to keep from having to get up at 2 in the morning,” and made the trip from Columbus to Wooster, Ohio, where he lectured in Arcadome Hall – “Roughing It” [MTL 5: 11-12n3].

January 7 Sunday – Sam telegraphed from Wooster, Ohio to William Dean Howells to solicit Bret Harte and “the other boys” to get up a fund for William Andrew Kendall (1831?-1876), a poet who was ill in New York, to gain his passage back to California. Sam claimed he didn’t know Kendall, but Harte did, having published several of his poems while editor of the Overland.

January 8 Monday – Sam gave the “Roughing It” lecture in Concert Hall, Salem, Ohio [MTPO].

He wrote from Salem to Livy.

“Well, slowly this lecturing penance drags toward the end. Heaven knows I shall be glad when I get far away from these country communities of wooden-heads. Whenever I want to go away from New England again, lecturing, please show these letters to me & bring me to my senses” [MTL 5: 14].

January 9 Tuesday – Sam lectured in Gray and Garrett’s Hall, Steubenville, Ohio – “Roughing It” [MTPO].

January 10 Wednesday – Sam wrote from Steubenville to Livy about his visit after the lecture to the Steubenville Female Seminary; the winning of passenger business by the railroads from steamboats; and novels he’d read and sent home.

January 11 Thursday – Sam left Wheeling in the afternoon and traveled to Pittsburgh, Pennsylvania, where he lectured in Mercantile Library Hall – “Roughing It.”

Afterward he finished his Jan. 10 to Redpath and also wrote Livy:

January 12 Friday – Sam lectured in Kittanning, Pennsylvania – “Roughing It.” Sam wrote from Kittanning to Livy before the lecture:

“Livy darling, this is a filthy, stupid, hateful Dutch village, like all Pennsylvania—& I have got to lecture to these leatherheads tonight, but shall leave for Pittsburgh at 3 in the morning, & spend Sunday in that black but delightful town” [MTL 5: 21-2].

January 13 Saturday – Sam had an open weekend and wrote a short note from Pittsburgh to Livy, sending clippings of favorable reviews. In the note he wrote that he’d just sent a “long dispatch,” which has been lost [MTL 5: 22].

Sam also sent a check and note to James Redpath for $124.69. The Lyceum charged speakers a 10% commission, and Sam owed back fees [26].

January 15 Monday – Sam’s lecture in Bellefonte, Pennsylvania was “backed” (canceled) by the committee there, so Sam spent a long weekend in Pittsburgh [MTL 5: 28].

Bill marked paid from Tracy & Co., Importers for “1 polished standard for Fire irons” $4 [MTP].

January 16 Tuesday – Sam was still in Pittsburgh when he wrote Livy: 

“…if ever I get through with this tour alive I never want to take another, even for a month.”

He took the train and lectured that evening in Opera House, Lock Haven, Pa. – “Roughing It” [MTL 5: 27].

January 17 Wednesday – Sam lectured in Milton, Pennsylvania – “Roughing It.” He wrote from either Lock Haven or Milton to James Redpath, turning down lectures after Feb.1 in Utica and Newburgh, New York [MTL 5: 28].

January 18 Thursday – Sam lectured in Court House, Harrisburg, Pennsylvania – “Roughing It.” Once again, Sam received mixed reviews:

January 19 Friday – Sam lectured in Fulton Opera House, Lancaster, Pennsylvania – “Roughing It.” Afterward, he returned to Harrisburg where he spent another open weekend. The reviews from Lancaster were unanimously positive [MTL 5: 30n3].

January 20 Saturday – Sam wrote from Harrisburg to Livy about the great success at Lancaster and miscellaneous matters. Livy had written that Joe Goodman and wife were in New York. Sam enclosed a Longfellow poem and one other unidentified [MTL 5: 28-9].

January 21 Sunday – In Harrisburg, Sam inscribed a copy of IA to Jane Findlay Shunk (1792-1878)

This book is given to
Miss Jane Findlay Shunk,
With the kindest regards of
Mark Twain
Harrisburgh, Jan. 21/72 [MTPO]

Note: The Findlays and the Shunks were old Pennsylvania political families.

January 22 Monday – Sam lectured in the Old Methodist Church, Carlisle, Pa. to about 600 – “Roughing It” [MTPO].

A contract was drawn between Sam and the American Publishing Co. [MTP]. Note: Sam probably signed it shortly after his return on Jan. 25.

January 23 Tuesday – Sam lectured in Maryland Institute, Baltimore, Maryland – “Roughing It.” Lecture manager Thomas B. Pugh asked Sam to deliver a second Philadelphia lecture on Feb.

January 24 Wednesday – Sam lectured to over 2,000 in Steinway Hall, New York City – “On Governor Nye,” a benefit for the Mercantile Library. Sam telegraphed from New York to James Redpath to tell Pugh that he would not lecture again this season [MTL 5: 31]. Though Sam had been in New York many times over the past few years, this was his first lecture there since May 1867, when he first spoke before an Eastern audience prior to leaving on the Quaker City excursion. The reviews praised the lectures. Sam stayed at the St. Nicholas Hotel.