I saw a tweet saying Croatia's center is located outside Croatia.
They computed it by taking the center of the minimal bounding rectangle.
To me a more natural approach would be to take centroid of the country, i.e. its center of mass.
So I set out to download all borders from Natural Earth, that provide 10 meter approximations to country borders as polygon(s).
As it turns, Croatia's mainland's center (below in blue) is located inside Croatia, but if we include enclaves and islands, it pushes the center (yellow) a few kilometers south, to Bosnia. A few other countries do not include their own centroid. One of them is Israel, whose center lies near Hebron: A full list is given below.
There's a somewhat interesting issue concerning locating the centroid of a large country, especially near a pole.
At first I just located the centroid of the resulting Mercator projection of the borders (i.e. x = lon, y = log(tan(PI/4 + lat/2))).
This projection distorts areas -- the closer you are to either poles, the larger you seem to be.
A more accurate approach would be to calculate the centroid of spherical polygons; I used this result.
The difference between the two approaches can be huge when countries include areas near the pole.
An example to that would be the US; after 2D projection, Alaska's area explodes disproportionally and pushes the centroid away (below, red); the true spherical centroid (blue) is somewhere around South Dakota. Here's a full list of all the territories Natural Earth gives. Click on one of them to get the map and its spherical centroid. Those who do not include their centroid are in bold.

Adjara Afghanistan Akrotiri Aland Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua Argentina Armenia Aruba Ashmore and Cartier Is. Australia Austria Azerbaijan Azores Bahamas Bahrain Baikonur Bajo Nuevo Bank Baker I. Bangladesh Barbados Barbuda Belarus Belize Benin Bermuda Bhutan Bolivia Botswana Bougainville Bouvet I. Br. Indian Ocean Ter. Brazil Brcko District British Virgin Is. Brunei Brussels Bulgaria Burkina Faso Burundi Cabo Verde Cambodia Cameroon Canada Caribbean Netherlands Cayman Is. Central African Rep. Chad Chile China Christmas I. Clipperton I. Cocos Is. Colombia Comoros Congo Cook Is. Coral Sea Is. Costa Rica Cote d'Ivoire Croatia Cuba Curacao Cyprus Cyprus U.N. Buffer Zone Czechia Dem. Rep. Congo Denmark Dhekelia Djibouti Dominica Dominican Rep. Ecuador Egypt El Salvador England Eq. Guinea Eritrea Estonia Ethiopia Faeroe Is. Falkland Is. Fed. of Bos. & Herz. Fiji Finland Flemish Fr. Polynesia Fr. S. Antarctic Lands France French Guiana Gabon Gambia Gaza Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-Bissau Guyana Haiti Heard I. and McDonald Is. Honduras Hong Kong Howland I. Hungary Iceland India Indonesia Iran Iraq Iraqi Kurdistan Ireland Isle of Man Israel Italy Jamaica Jan Mayen I. Japan Jarvis I. Jersey Johnston Atoll Jordan Kazakhstan Kenya Kingman Reef Kiribati Korean DMZ (north) Korean DMZ (south) Kosovo Kuwait Kyrgyzstan Laos Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Macedonia Madagascar Madeira Malawi Malaysia Maldives Mali Malta Marshall Is. Martinique Mauritania Mauritius Mayotte Mexico Micronesia Midway Is. Moldova Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar N. Cyprus N. Ireland N. Mariana Is. Namibia Nauru Navassa I. Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island North Korea Norway Oman Pakistan Palau Palmyra Atoll Panama Papua New Guinea Paracel Is. Paraguay Peru Philippines Pitcairn Is. Poland Portugal Puerto Rico Puntland Qatar Reunion Romania Russia Rwanda S. Geo. and the Is. S. Sudan Saint Helena Saint Lucia Samoa San Marino Sao Tome and Principe Saudi Arabia Scarborough Reef Scotland Senegal Serbia Serranilla Bank Seychelles Siachen Glacier Sierra Leone Singapore Sint Maarten Slovakia Slovenia Solomon Is. Somalia Somaliland South Africa South Korea Spain Spratly Is. Sri Lanka St-Barthelemy St-Martin St. Kitts and Nevis St. Pierre and Miquelon St. Vin. and Gren. Sudan Suriname Svalbard Is. Sweden Switzerland Syria Taiwan Tajikistan Tanzania Thailand Timor-Leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Is. Tuvalu U.S. Virgin Is. UNDOF Zone USNB Guantanamo Bay Uganda Ukraine United Arab Emirates United States of America Uruguay Uzbekistan Vanuatu Vatican Venezuela Vietnam Vojvodina W. Sahara Wake Atoll Wales Wallis and Futuna Is. Walloon West Bank Yemen Zambia Zanzibar Zimbabwe eSwatini